Shape sensitivity analysis of the Hardy constant

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• 作者：Gerassimos Barbatis^a ; Pier Domenico Lamberti^b ; ^{lamberti@math.unipd.it" class="auth_mail}
• 关键词：26D15 ; 35P15 ; 35P30
• 刊名：Nonlinear Analysis
• 出版年：July, 2014
• 年：2014
• 卷：103
• 期：Complete
• 页码：98-112
• 全文大小：448 K

文摘

We consider the Hardy constant associated with a domain in the -dimensional Euclidean space and we study its variation upon perturbation of the domain. We prove a Fr茅chet differentiability result and establish a Hadamard-type formula for the corresponding derivatives. We also prove a stability result for the minimizers of the Hardy quotient. Finally, we prove stability estimates in terms of the Lebesgue measure of the symmetric difference of domains.