Problems involving $p$-Laplacian type equations and measures
نویسندگان
چکیده
منابع مشابه
p-Laplacian Type Equations Involving Measures
This is a survey on problems involving equations −divA(x,∇u) = μ, where μ is a Radon measure and A : Rn ×Rn → Rn verifies Leray-Lions type conditions. We shall discuss a potential theoretic approach when the measure is nonnegative. Existence and uniqueness, and different concepts of solutions are discussed for general signed measures. 2000 Mathematics Subject Classification: 35J60, 31C45.
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Under suitable assumptions on the potential of the nonlinearity, we study the existence and multiplicity of solutions for a Steklov problem involving the p(x)-Laplacian. Our approach is based on variational methods.
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In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional J (u) = ∂Ω f(x)u dHN−1 over some admissible class of loads f where u is the (unique) solution to the problem −∆pu + |u|p−2u = 0 in Ω with |∇u|p−2uν = f on ∂Ω.
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Given a bounded domain Ω ⊂ R and numbers p > 1, α ≥ 0, A ∈ [0, |Ω|], consider the following optimization problem: find a subset D ⊂ Ω, of measure A, for which the first eigenvalue of the operator −∆p + αχD φp with the Dirichlet boundary condition is as small as possible. We prove the existence of optimal solutions and study their qualitative properties. We also obtain the radial symmetry of opt...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2002
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2002.134164