Sharp Gagliardo–Nirenberg Inequalities via p-Laplacian Type Equations
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.
متن کاملLiapunov-type Integral Inequalities for P-laplacian Dynamic Equations on Time Scales
In this paper, we estimate Liapunov-type integral inequalities for a single, cycled, and coupled dynamic system of one-dimensional p-Laplacian problems with weight functions having stronger singularities.
متن کاملLYAPUNOV–TYPE INEQUALITIES FOR HIGHER–ORDER DIFFERENTIAL EQUATIONS WITH ONE–DIMENSIONAL p–LAPLACIAN
In this paper, we establish Lyapunov-type inequalities for a single higher-order differential equation, a cycled system and a coupled system with one-dimensional p -Laplacian. Our result generalize some given results.
متن کاملPOHOZAEV-TYPE INEQUALITIES AND NONEXISTENCE RESULTS FOR NON C SOLUTIONS OF p(x)-LAPLACIAN EQUATIONS
In this article we obtain a Pohozaev-type inequality for Sobolev spaces with variable exponents. This inequality is used for proving the nonexistence of nontrivial weak solutions for the Dirichlet problem −∆p(x)u = |u|q(x)−2u, x ∈ Ω u(x) = 0, x ∈ ∂Ω, with non-standard growth. Our results extend those obtained by Ôtani [16].
متن کاملSOME OPTIMIZATION PROBLEMS FOR p−LAPLACIAN TYPE EQUATIONS
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Differential Equations and Applications NoDEA
سال: 2008
ISSN: 1021-9722,1420-9004
DOI: 10.1007/s00030-008-7021-4