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− |2 2) )( / p 2 − ∇ 2) u / 2 + ∇c u(x )) −|u div(|p−2 cu (x )· |un _|p = − 0 2u) = 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

Maria Francesca Betta
Membro del Collaboration Group
;
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− |2 2) )( / p 2 − ∇ 2) u / 2 + ∇c u(x )) −|u div(|p−2 cu (x )· |un _|p = − 0 2u) = 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/11367/64573
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