On viscosity and weak solutions for non-homogeneous p-Laplace equations
نویسندگان
چکیده
منابع مشابه
Weak and Viscosity Solutions of the Fractional Laplace Equation
Aim of this paper is to show that weak solutions of the following fractional Laplacian equation { (−∆)su = f in Ω u = g in Rn \ Ω are also continuous solutions (up to the boundary) of this problem in the viscosity sense. Here s ∈ (0, 1) is a fixed parameter, Ω is a bounded, open subset of Rn (n > 1) with C2-boundary, and (−∆)s is the fractional Laplacian operator, that may be defined as (−∆)u(x...
متن کاملA Non-homogeneous P-laplace Equation in Border Case
Searching minimizers of functions on the convenient level set of the constrain function we obtain weak solutions of a non-homogenuous p-Laplace equation in border case without using the regularity results of linear elliptic equations .
متن کاملSTABILITY OF POSITIVE SOLUTIONS TO p&2–LAPLACE TYPE EQUATIONS
In this article, we first show the existence of a positive solution to { −Δpu−αΔu = λ(u− f (u)) in Ω, u = 0 on ∂Ω, by the method of lower and upper solutions and then under certain conditions on f , we show the stability of positive solution. Mathematics subject classification (2010): 35J92, 35B35, 35B05.
متن کاملWeak Dynamic Programming Principle for Viscosity Solutions
We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the measurable selection argument. In the Markov case, our result is tailor-maid for the derivation of the dynamic programming equation in the sense of viscosity solutions.
متن کاملEXISTENCE OF SOLUTIONS FOR A p(x)-LAPLACIAN NON-HOMOGENEOUS EQUATIONS
We study the boundary value problem − div(|∇u|p(x)−2∇u) = f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in RN . Our attention is focused on the cases when f(x, u) = ±(−λ|u|p(x)−2u+ |u|q(x)−2u), where p(x) < q(x) < N · p(x)/(N − p(x)) for x in 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: Advances in Nonlinear Analysis
سال: 2017
ISSN: 2191-9496,2191-950X
DOI: 10.1515/anona-2017-0005