{"id":3644,"date":"2026-05-21T14:51:15","date_gmt":"2026-05-21T06:51:15","guid":{"rendered":"https:\/\/deptweb.cycu.edu.tw\/qic\/?page_id=3644"},"modified":"2026-05-21T15:06:09","modified_gmt":"2026-05-21T07:06:09","slug":"%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01","status":"publish","type":"page","link":"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/","title":{"rendered":"\u6578\u7406\u4eba\u6587029_01"},"content":{"rendered":"\n

\u7d04\u675f\u6620\u5c04\u8207\u81ea\u7531\u908a\u754c<\/strong><\/h1>\n\n\n\n

\u672c\u6587\u9810\u89bd<\/a><\/p>\n\n\n\n

\u4f5c\u8005<\/strong>\u3000\u5e15\u83f2\u52a0\u5229(Alessio Figalli)\u3001\u683c\u62c9(Andr\u00e9 Guerra)\u3001\u91d1\u6210\u6f22(Sunghan Kim) \u8207 \u6c99\u683c\u5229\u5b89(Henrik Shahgholian)<\/p>\n\n\n\n

\u4f5c\u8005\u7c21\u4ecb<\/strong>
\u83f2\u52a0\u5229\u662f\u4e00\u4f4d\u7fa9\u5927\u5229\u6578\u5b78\u5bb6,\u4e3b\u8981\u7684\u7814\u7a76\u9818\u57df\u662f\u8b8a\u5206\u5b78\u548c\u504f\u5fae\u5206\u65b9\u7a0b\u3002\u56e0\u5176\u6700\u4f73\u50b3\u8f38\u554f\u984c\u53ca\u5176\u5728\u504f\u5fae\u5206\u65b9\u7a0b\u3001\u5ea6\u91cf\u5e7e\u4f55\u8207\u6a5f\u7387\u7684\u61c9\u7528\u5de5\u4f5c\u8ca2\u737b\u800c\u805e\u540d,\u4e26\u56e0\u6b64\u65bc 2018 \u5e74\u7372\u9812\u8cbb\u723e\u8332\u734e\u3002\u4ed6\u73fe\u5728\u662f\u8607\u9ece\u4e16\u806f\u90a6\u7406\u5de5\u5b78\u9662(ETH Z\u00fcrich)\u7684\u8b1b\u5ea7\u6559\u6388\u3002
\u683c\u62c9\u662f\u4e00\u4f4d\u8461\u8404\u7259\u6578\u5b78\u5bb6,\u4e3b\u8981\u7684\u7814\u7a76\u9818\u57df\u662f\u8b8a\u5206\u5b78\u548c\u504f\u5fae\u5206\u65b9\u7a0b\u3002\u4ed6\u73fe\u5728\u662f\u8607\u9ece\u4e16\u806f\u90a6\u7406\u5de5\u5b78\u9662\u7406\u8ad6\u7814\u7a76\u6240\u7684\u521d\u7d1a\u7814\u7a76\u54e1,\u6307\u5c0e\u6559\u6388\u662f\u83f2\u52a0\u5229\u3002
\u91d1\u6210\u6f22\u662f\u4e00\u4f4d\u97d3\u570b\u6578\u5b78\u5bb6,\u73fe\u5728\u662f\u745e\u5178\u70cf\u666e\u6492\u62c9\u5927\u5b78(Uppsala University)\u7684\u535a\u58eb\u5f8c,\u4e3b\u8981\u7684\u7814\u7a76\u9818\u57df\u662f\u504f\u5fae\u5206\u65b9\u7a0b\u3002
\u6c99\u683c\u5229\u5b89\u662f\u745e\u5178\u7687\u5bb6\u7406\u5de5\u5b78\u9662(KTH Royal Institute of Technology)\u7684\u6578\u5b78\u6559\u6388,\u4ed6\u7684\u7814\u7a76\u4e3b\u8981\u96c6\u4e2d\u5728\u975e\u7dda\u6027\u504f\u5fae\u5206\u65b9\u7a0b\u7684\u5206\u6790,\u7279\u5225\u8457\u91cd\u65bc\u81ea\u7531\u908a\u754c\u554f\u984c\u53ca\u5176\u6b63\u5247\u6027\u7406\u8ad6\u3002<\/p>\n\n\n\n

\u8b6f\u8005<\/strong>\u3000\u738b\u590f\u8072<\/p>\n\n\n\n

\u8b6f\u8005\u7c21\u4ecb<\/strong>
\u738b\u590f\u8072\u70ba\u967d\u660e\u4ea4\u901a\u5927\u5b78\u61c9\u7528\u6578\u5b78\u7cfb\u526f\u6559\u6388\u3002<\/p>\n\n\n\n

\u672c\u6587\u51fa\u8655<\/strong>\u3000\u672c\u6587\u8b6f\u81eaAlessio Figalli, Andr\u00e9 Guerra, Sunghan Kim, and Henrik Shahgholian, \u201cConstraint Maps and Free Boundaries\u201d, ]Notices of the AMS 72\uff082025\uff09No. 5, AMS\u3002\u00a9 American Mathematical Society 2008. All rights reserved\u3002\u611f\u8b1d AMS \u8207\u4f5c\u8005\u5011\u540c\u610f\u8f49\u8f09\u7ffb\u8b6f\u3002<\/p>\n\n\n\n

\u5ef6\u4f38\u95b1\u8b80<\/strong>
\u672c\u520a\u7b2c27\u671f\u7684\u3008\u4e00\u4f4d\u975e\u5e38\u591a\u7522\u7684\u6578\u5b78\u5bb6\u2500\u2500\u5361\u6cd5\u745e\u91cc\u3009\u4e00\u6587\uff0c\u5728\u9019\u7bc7\u6587\u7ae0\u88e1\u4e5f\u6709\u95dc\u65bc\u81ea\u7531\u908a\u754c\u554f\u984c\u6b63\u5247\u6027\u7406\u8ad6\u7684\u4ecb\u7d39\u3002<\/p>\n\n\n\n

\u53c3\u8003\u6587\u737b<\/strong>
[Caf98] L. A. Caffarelli, The obstacle problem revisited, J. Fourier Anal. Appl. 4 (1998), no. 4-5, 383\u2013402.
[Caf77] Luis A. Caffarelli, The regularity of free boundaries in higher dimensions, Acta Math. 139 (1977),
no. 3-4, 155\u2013184.
[Cou77] R. Courant, Dirichlet\u2019s principle, conformal mapping, and minimal surfaces, Springer, New York,
NY, 1977.
[DF86] F. Duzaar and M. Fuchs, Optimal regularity theorems for variational problems with obstacles,
Manuscripta Math. 56 (1986), no. 2, 209\u2013234.
[Duz87] Frank Duzaar, Variational inequalities and harmonic mappings, J. Reine Angew. Math. 374 (1987),
39\u201360.
[FGKS23] A. Figalli, A. Guerra, S. Kim, and S. Shahgholian, Constraint maps with free boundaries: the
Bernoulli case, to appear in J. Eur. Math. Soc. (2023).
[FGKS24] A. Figalli, A. Guerra, S. Kim, and S. Shahgholian, Constraint maps: singularities vs free
boundaries (2024).
[FKS24] A. Figalli, S. Kim, and H. Shahgholian, Constraint maps with free boundaries: the obstacle case,
Arch. Ration. Mech. Anal. 248 (2024), no. 5, 36pp.
[FROS20] A. Figalli, X. Ros-Oton, and J. Serra, Generic regularity of free boundaries for the obstacle
problem, Publ. Math. IH\u00c9S 132 (2020), no. 1, 181\u2013292.
[FW89] Martin Fuchs and Michael Wiegner, The regularity of minima of variational problems with graph
obstacles, Arch. Math. (Basel) 53 (1989), no. 1, 75\u201381.
[Ger16] J. D. Gergonne, Questions propos\u00e9es, Ann. Math. Pure Appl. 7 (1816), no. 68, 99\u2013100.
[Hil72] S. Hildebrandt, On the regularity of solutions of two-dimensional variational problems with
obstructions, Commun. Pure Appl. Math. 25 (1972), no. 4, 479\u2013496.
[Luc88] Stephan Luckhaus, Partial H\u00f6lder continuity for minima of certain energies among maps into a
Riemannian manifold, Indiana Univ. Math. J. 37 (1988), no. 2, 349\u2013367.
[Mon03] R. Monneau, On the number of singularities for the obstacle problem in two dimensions, J. Geom.
Anal. 13 (2003), no. 2, 359\u2013389.
[Mor48] C. B. Morrey, The problem of plateau on a Riemannian manifold, Ann. Math. 49 (1948), no. 4, 807.
[NV17] Aaron Naber and Daniele Valtorta, Rectifiable-Reifenberg and the regularity of stationary and
minimizing harmonic maps, Ann. of Math. (2) 185 (2017), no. 1, 131\u2013227.
[Sch77] David G. Schaeffer, Some examples of singularities in a free boundary, Ann. Scuola Norm. Sup.
Pisa Cl. Sci. (4) 4 (1977), no. 1, 133\u2013144.
[Sch72] H. A. Schwarz, Fortgesetzte untersuchungen \u00fcber specielle minimalfl\u00e4chen, Buchdruckerei der
K\u00f6niglichen Akademie der Wissenschaften (1872), 126\u2013148.
[SU82] Richard Schoen and Karen Uhlenbeck, A regularity theory for harmonic maps, J. Differential
Geometry 17 (1982), no. 2, 307\u2013335.
[Tom71] Friedrich Tomi, Minimal surfaces and surfaces of prescribed mean curvature spanned over
obstacles, Math. Ann. 190 (1970\/71), 248\u2013264.<\/p>\n","protected":false},"excerpt":{"rendered":"

\u7d04\u675f\u6620\u5c04\u8207\u81ea\u7531\u908a\u754c \u672c\u6587\u9810\u89bd \u4f5c\u8005\u3000\u5e15\u83f2\u52a0\u5229(Alessio Figalli)\u3001\u683c\u62c9(Andr\u00e9 Guerra […]<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":3598,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-3644","page","type-page","status-publish","hentry","entry"],"yoast_head":"\n\u6578\u7406\u4eba\u6587029_01 - \u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/deptweb.cycu.edu.tw\/qic\/\u6578\u7406\u4eba\u6587\/\u6578\u7406\u4eba\u6587029\/\u6578\u7406\u4eba\u6587029_01\/\" \/>\n<meta property=\"og:locale\" content=\"zh_TW\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u6578\u7406\u4eba\u6587029_01 - \u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u7d04\u675f\u6620\u5c04\u8207\u81ea\u7531\u908a\u754c \u672c\u6587\u9810\u89bd \u4f5c\u8005\u3000\u5e15\u83f2\u52a0\u5229(Alessio Figalli)\u3001\u683c\u62c9(Andr\u00e9 Guerra […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/deptweb.cycu.edu.tw\/qic\/\u6578\u7406\u4eba\u6587\/\u6578\u7406\u4eba\u6587029\/\u6578\u7406\u4eba\u6587029_01\/\" \/>\n<meta property=\"og:site_name\" content=\"\u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3\" \/>\n<meta property=\"article:modified_time\" content=\"2026-05-21T07:06:09+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u9810\u4f30\u95b1\u8b80\u6642\u9593\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 \u5206\u9418\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/\",\"url\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/\",\"name\":\"\u6578\u7406\u4eba\u6587029_01 - \u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/#website\"},\"datePublished\":\"2026-05-21T06:51:15+00:00\",\"dateModified\":\"2026-05-21T07:06:09+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/#breadcrumb\"},\"inLanguage\":\"zh-TW\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u6578\u7406\u4eba\u6587\",\"item\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u6578\u7406\u4eba\u6587029\",\"item\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"\u6578\u7406\u4eba\u6587029_01\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/#website\",\"url\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/\",\"name\":\"\u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3\",\"description\":\"\u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/deptweb.cycu.edu.tw\/qic\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"zh-TW\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u6578\u7406\u4eba\u6587029_01 - \u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/deptweb.cycu.edu.tw\/qic\/\u6578\u7406\u4eba\u6587\/\u6578\u7406\u4eba\u6587029\/\u6578\u7406\u4eba\u6587029_01\/","og_locale":"zh_TW","og_type":"article","og_title":"\u6578\u7406\u4eba\u6587029_01 - \u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3","og_description":"\u7d04\u675f\u6620\u5c04\u8207\u81ea\u7531\u908a\u754c \u672c\u6587\u9810\u89bd \u4f5c\u8005\u3000\u5e15\u83f2\u52a0\u5229(Alessio Figalli)\u3001\u683c\u62c9(Andr\u00e9 Guerra […]","og_url":"https:\/\/deptweb.cycu.edu.tw\/qic\/\u6578\u7406\u4eba\u6587\/\u6578\u7406\u4eba\u6587029\/\u6578\u7406\u4eba\u6587029_01\/","og_site_name":"\u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3","article_modified_time":"2026-05-21T07:06:09+00:00","twitter_card":"summary_large_image","twitter_misc":{"\u9810\u4f30\u95b1\u8b80\u6642\u9593":"3 \u5206\u9418"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/","url":"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/","name":"\u6578\u7406\u4eba\u6587029_01 - \u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/deptweb.cycu.edu.tw\/qic\/#website"},"datePublished":"2026-05-21T06:51:15+00:00","dateModified":"2026-05-21T07:06:09+00:00","breadcrumb":{"@id":"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/#breadcrumb"},"inLanguage":"zh-TW","potentialAction":[{"@type":"ReadAction","target":["https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029_01\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u6578\u7406\u4eba\u6587","item":"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/"},{"@type":"ListItem","position":2,"name":"\u6578\u7406\u4eba\u6587029","item":"https:\/\/deptweb.cycu.edu.tw\/qic\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87\/%e6%95%b8%e7%90%86%e4%ba%ba%e6%96%87029\/"},{"@type":"ListItem","position":3,"name":"\u6578\u7406\u4eba\u6587029_01"}]},{"@type":"WebSite","@id":"https:\/\/deptweb.cycu.edu.tw\/qic\/#website","url":"https:\/\/deptweb.cycu.edu.tw\/qic\/","name":"\u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3","description":"\u4e2d\u539f\u5927\u5b78\u91cf\u5b50\u8cc7\u8a0a\u4e2d\u5fc3","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/deptweb.cycu.edu.tw\/qic\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"zh-TW"}]}},"_links":{"self":[{"href":"https:\/\/deptweb.cycu.edu.tw\/qic\/wp-json\/wp\/v2\/pages\/3644"}],"collection":[{"href":"https:\/\/deptweb.cycu.edu.tw\/qic\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/deptweb.cycu.edu.tw\/qic\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/deptweb.cycu.edu.tw\/qic\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/deptweb.cycu.edu.tw\/qic\/wp-json\/wp\/v2\/comments?post=3644"}],"version-history":[{"count":10,"href":"https:\/\/deptweb.cycu.edu.tw\/qic\/wp-json\/wp\/v2\/pages\/3644\/revisions"}],"predecessor-version":[{"id":3658,"href":"https:\/\/deptweb.cycu.edu.tw\/qic\/wp-json\/wp\/v2\/pages\/3644\/revisions\/3658"}],"up":[{"embeddable":true,"href":"https:\/\/deptweb.cycu.edu.tw\/qic\/wp-json\/wp\/v2\/pages\/3598"}],"wp:attachment":[{"href":"https:\/\/deptweb.cycu.edu.tw\/qic\/wp-json\/wp\/v2\/media?parent=3644"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}