In the present paper we prove uniqueness results for solutions to a class of Neumann boundary value problems whose prototype is −(1 div((1+ |∇ +u|2 |∇)(p u− |22) )(/p2−∇2)u/2+ ∇c u(x )) −|u div(|p−2 cu (x )· |un _|p=−02u) = f in Ω, on ∂Ω, where Ω is a bounded domain of RN, N ≥ 2, with Lipschitz boundary, 1 < p < N , n is the outer unit normal to ∂Ω, the datum f belongs to L(p∗)(Ω) or to L1(Ω) and satisfies the compatibility condition Ω f dx = 0. Finally the coefficient c(x) belongs to an appropriate Lebesgue space.

UNIQUENESS FOR NEUMANN PROBLEMS FOR NONLINEAR ELLIPTIC EQUATIONS

Anna Mercaldo
2019

Abstract

In the present paper we prove uniqueness results for solutions to a class of Neumann boundary value problems whose prototype is −(1 div((1+ |∇ +u|2 |∇)(p u− |22) )(/p2−∇2)u/2+ ∇c u(x )) −|u div(|p−2 cu (x )· |un _|p=−02u) = f in Ω, on ∂Ω, where Ω is a bounded domain of RN, N ≥ 2, with Lipschitz boundary, 1 < p < N , n is the outer unit normal to ∂Ω, the datum f belongs to L(p∗)(Ω) or to L1(Ω) and satisfies the compatibility condition Ω f dx = 0. Finally the coefficient c(x) belongs to an appropriate Lebesgue space.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/728351
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