A uniqueness result for a class of non-strictly convex variational problems

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• 作者：Luca Lussardi^a ; ^{luca.lussardi@unicatt.it" class="auth_mail" title="E-mail the corresponding author} ; ; Elvira Mascolo^b ; ^{mascolo@math.unifi.it" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：Lipschitz functions ; Level sets
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1687-1694
• 全文大小：306 K

文摘

Let Ω be a smooth domain in R²${\mathbb{R}}^2$, we prove that if 975c2a6b3d81303d0fb9647348d70bf" title="Click to view the MathML source">g:[0,+∞)→[0,+∞]$g:[0,+\infty )\to [0,+\infty ]$ is convex with g(0)<g(t)$g(0)<g(t)$ whenever 8f5ff2f90d8fedb0c0f0a2204f1eb" title="Click to view the MathML source">t>0$t>0$ then there exists an unique minimizer e5ecbfe6b1e990de524d6e23ca" title="Click to view the MathML source">u∈C^0,1(Ω)$u\in C^{0,1}(\mathrm{\Omega })$ of the functional e6b35f093c67d5728d110ba740e7">$u\mapsto {\int }_{\mathrm{\Omega }}g(|\mathrm{\nabla }u|)dxdy$ among all Lipschitz-continuous functions that assume the same value of u on ∂Ω.