{"id":193791,"date":"2024-07-31T02:25:25","date_gmt":"2024-07-31T07:25:25","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2024\/07\/on-the-dirichlet-and-serrin-problems-for-the-inhomogeneous-infinity-laplacian-in-convex-domains-regularity-and-geometric-results"},"modified":"2024-07-31T02:25:25","modified_gmt":"2024-07-31T07:25:25","slug":"on-the-dirichlet-and-serrin-problems-for-the-inhomogeneous-infinity-laplacian-in-convex-domains-regularity-and-geometric-results","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2024\/07\/on-the-dirichlet-and-serrin-problems-for-the-inhomogeneous-infinity-laplacian-in-convex-domains-regularity-and-geometric-results","title":{"rendered":"On the Dirichlet and Serrin Problems for the Inhomogeneous Infinity Laplacian in Convex Domains: Regularity and Geometric Results"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/on-the-dirichlet-and-serrin-problems-for-the-inhomogeneous-infinity-laplacian-in-convex-domains-regularity-and-geometric-results.jpg\"><\/a><\/p>\n<p>Given an open bounded subset \u03a9 of $mathbbR^n$$ R n, which is convex and satisfies an interior sphere condition, we consider the pde $-\\Delta_infty u = 1$$ \u2014 \u0394 \u221e u = 1 in \u03a9, subject to the homogeneous boundary condition u = 0 on \u2202\u03a9. We prove that the unique solution to this Dirichlet problem is power-concave (precisely, 3\/4 concave) and it is of class C 1(\u03a9).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given an open bounded subset \u03a9 of $mathbbR^n$$ R n, which is convex and satisfies an interior sphere condition, we consider the pde $-\\Delta_infty u = 1$$ \u2014 \u0394 \u221e u = 1 in \u03a9, subject to the homogeneous boundary condition u = 0 on \u2202\u03a9. We prove that the unique solution to this Dirichlet [\u2026]<\/p>\n","protected":false},"author":513,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1497],"tags":[],"class_list":["post-193791","post","type-post","status-publish","format-standard","hentry","category-energy"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/193791","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/513"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=193791"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/193791\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=193791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=193791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=193791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}