A concave-convex problem with a variable operator

A concave-convex problem with a variable operator

We study the following elliptic problem \(-A(u) = \lambda u^q\) with Dirichlet boundary conditions, where \(A(u) (x) = \Delta u (x) \chi_{D_1} (x)+ \Delta_p u(x) \chi_{D_2}(x)\) is the Laplacian in one part of the domain, \(D_1\), and the \(p-\)Laplacian (with \(p>2\)) in the rest of the domain,...

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Veröffentlicht in:arXiv.org 2017-03
Hauptverfasser: Molino, Alexis, Rossi, Julio D
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Dirichlet problem
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Zusammenfassung:We study the following elliptic problem \(-A(u) = \lambda u^q\) with Dirichlet boundary conditions, where \(A(u) (x) = \Delta u (x) \chi_{D_1} (x)+ \Delta_p u(x) \chi_{D_2}(x)\) is the Laplacian in one part of the domain, \(D_1\), and the \(p-\)Laplacian (with \(p>2\)) in the rest of the domain, \(D_2 \). We show that this problem exhibits a concave-convex nature for \(1
ISSN:2331-8422