{"id":41017,"date":"2024-09-25T12:48:30","date_gmt":"2024-09-25T12:48:30","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-c1%ce%b1-%d9%85%d9%86%d8%b8%d9%85-%d8%a8%d9%88%d8%af%d9%86-%d9%85%d8%b3%d8%a7%d8%a6%d9%84-%d8%aa%d8%ba\/"},"modified":"2024-09-25T12:48:58","modified_gmt":"2024-09-25T12:48:58","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-c1%ce%b1-%d9%85%d9%86%d8%b8%d9%85-%d8%a8%d9%88%d8%af%d9%86-%d9%85%d8%b3%d8%a7%d8%a6%d9%84-%d8%aa%d8%ba","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-c1%ce%b1-%d9%85%d9%86%d8%b8%d9%85-%d8%a8%d9%88%d8%af%d9%86-%d9%85%d8%b3%d8%a7%d8%a6%d9%84-%d8%aa%d8%ba\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 C^{1,\u03b1} \u0645\u0646\u0638\u0645 \u0628\u0648\u062f\u0646 \u0645\u0633\u0627\u0626\u0644 \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0628\u0627 \u06cc\u06a9 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a \u062a\u062d\u062f\u0628"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\n$C^{1,\u03b1}$ regularity of variational problems with a convexity constraint<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 C^{1,\u03b1} \u0645\u0646\u0638\u0645 \u0628\u0648\u062f\u0646 \u0645\u0633\u0627\u0626\u0644 \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0628\u0627 \u06cc\u06a9 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a \u062a\u062d\u062f\u0628<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nLing Wang, Bin Zhou<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n15<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nAnalysis of PDEs,\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 PDES ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 7 March, 2024; originally announced March 2024. , Comments: 15 pages<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 7 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u0646\u0638\u0631\u0627\u062a: 15 \u0635\u0641\u062d\u0647<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

In this paper, we establish the interior $C^{1,\u03b1}$ regularity of minimizers of a class of functionals with a convexity constraint, which includes the principal-agent problems studied by Figalli-Kim-McCann (\\textit{J. Econom. Theory} \\textbf{146} (2011), no. 2, 454-478). The $C^{1,1}$ regularity was previously proved by Caffarelli-Lions in an unpublished note when the cost is quadratic, and recently extended to the case where the cost is uniformly convex with respect to a general preference function by McCann-Rankin-Zhang(\\textit{arXiv:2303.04937v3}). Our main result does not require the uniform convexity assumption on the cost function. In particular, we show that the solutions to the principal-agent problems with $q$-power cost are $C^{1,\\frac{1}{q-1}}$ when $q > 2$ and $C^{1,1}$ when $1\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u060c \u0645\u0627 \u062f\u0627\u062e\u0644\u06cc $ c^{1 \u060c \u03b1} $ \u0645\u0646\u0638\u0645 \u0627\u0632 \u0645\u06cc\u0646\u06cc\u0645\u06cc\u0632\u0631\u0647\u0627\u06cc \u06cc\u06a9 \u06a9\u0644\u0627\u0633 \u0627\u0632 \u06a9\u0627\u0631\u06a9\u0631\u062f\u0647\u0627\u06cc \u0628\u0627 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a \u0645\u062d\u062f\u0628 \u0631\u0627 \u062a\u0639\u06cc\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u060c \u06a9\u0647 \u0634\u0627\u0645\u0644 \u0645\u0634\u06a9\u0644\u0627\u062a \u0627\u0635\u0644\u06cc \u0639\u0627\u0645\u0644 \u0645\u0648\u0631\u062f \u0645\u0637\u0627\u0644\u0639\u0647 \u062a\u0648\u0633\u0637 figalli-kim-mccann \u0627\u0633\u062a (\\ textit {j.\u0627\u0642\u062a\u0635\u0627\u062f. \u062a\u0626\u0648\u0631\u06cc} \\ TextBf {146} (2011) \u060c \u0634\u0645\u0627\u0631\u0647 2 \u060c 454-478).$ c^{1\u060c1} $ \u0642\u0628\u0644\u0627\u064b \u062a\u0648\u0633\u0637 \u06a9\u0627\u0641\u0627\u0631\u0644\u06cc-\u0634\u06cc\u0631\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06cc\u0627\u062f\u062f\u0627\u0634\u062a \u0645\u0646\u062a\u0634\u0631 \u0646\u0634\u062f\u0647 \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0647\u0632\u06cc\u0646\u0647 \u062f\u0631\u062c\u0647 \u062f\u0648\u0645 \u0627\u0633\u062a \u060c \u0627\u062b\u0628\u0627\u062a \u0634\u062f\u0647 \u0628\u0648\u062f \u060c \u0648 \u0627\u062e\u06cc\u0631\u0627\u064b \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f \u06af\u0633\u062a\u0631\u0634 \u06cc\u0627\u0641\u062a\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0647\u0632\u06cc\u0646\u0647 \u0628\u0647 \u0637\u0648\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0645\u062d\u062f\u0628 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u06cc\u06a9 \u0639\u0645\u0644\u06a9\u0631\u062f \u0627\u0648\u0644\u0648\u06cc\u062a \u06a9\u0644\u06cc \u062a\u0648\u0633\u0637 \u0645\u06a9 \u06a9\u0627\u0646-Rankin-Zhang (\\ textit {arxiv: 2303.04937v3}).\u0646\u062a\u06cc\u062c\u0647 \u0627\u0635\u0644\u06cc \u0645\u0627 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u0641\u0631\u0636 \u0645\u062d\u062f\u0628 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062f\u0631 \u0639\u0645\u0644\u06a9\u0631\u062f \u0647\u0632\u06cc\u0646\u0647 \u0646\u062f\u0627\u0631\u062f.\u0628\u0647 \u0637\u0648\u0631 \u062e\u0627\u0635 \u060c \u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc \u0645\u0634\u06a9\u0644\u0627\u062a \u0627\u0635\u0644\u06cc \u0639\u0627\u0645\u0644 \u0628\u0627 \u0647\u0632\u06cc\u0646\u0647 $ $ -power $ c^{1 \u060c \\ frac {1} {q-1}} $ \u0627\u0633\u062a \u06a9\u0647 $ q> 2 $ \u0648 $ c^{1\u060c1} $ \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 1 $ \n","protected":false},"excerpt":{"rendered":"

\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc $C^{1,\u03b1}$ regularity of variational problems with a convexity constraint \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 […]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"closed","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[15,21],"product_tag":[378,379],"class_list":{"0":"post-41017","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-15","7":"product_cat-21","8":"product_tag-analysis-of-pdes","9":"product_tag----pdes","10":"pmpro-has-access","11":"desktop-align-left","12":"tablet-align-left","13":"mobile-align-left","15":"first","16":"instock","17":"downloadable","18":"shipping-taxable","19":"purchasable","20":"product-type-simple"},"yoast_head":"\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 C^{1,\u03b1} \u0645\u0646\u0638\u0645 \u0628\u0648\u062f\u0646 \u0645\u0633\u0627\u0626\u0644 \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0628\u0627 \u06cc\u06a9 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a \u062a\u062d\u062f\u0628 - 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