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Minimization of functionals of the gradient by Baire's theorem

TitleMinimization of functionals of the gradient by Baire's theorem
Publication TypeJournal Article
Year of Publication2000
AuthorsZagatti, S
JournalSIAM J. Control Optim. 38 (2000) 384-399
Abstract

We give sufficient conditions for the existence of solutions of the minimum problem $$ {\mathcal{P}}_{u_0}: \qquad \hbox{Minimize}\quad \int_\Omega g(Du(x))dx, \quad u\in u_0 + W_0^{1,p}(\Omega,{\mathbb{R}}), $$ based on the structure of the epigraph of the lower convex envelope of g, which is assumed be lower semicontinuous and to grow at infinity faster than the power p with p larger than the dimension of the space. No convexity conditions are required on g, and no assumptions are made on the boundary datum $u_0\in W_0^{1,p}(\Omega,\mathbb{R})$.

URLhttp://hdl.handle.net/1963/3511
DOI10.1137/S0363012998335206

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