## Abstract This paper is devoted to the existence and regularity of the homogenous Dirichlet boundary value problem for a singular nonlinear elliptic equation with natural growth in the gradient. By certain transformations, the problem can be transformed formally into either a Dirichlet problem or
Nonlinear elliptic equations with natural growth in the gradient and source terms in Lorentz spaces
✍ Scribed by Ferone, Vincenzo; Murat, François
- Book ID
- 121348438
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 343 KB
- Volume
- 256
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We prove approximation and compactness results in inhomogeneous Orlicz-Sobolev spaces and look at, as an application, the Cauchy-Dirichlet equation u +A(u)+g(x, t, u, ∇u)=f ∈ W -1,x E M , where A is a Leray-Lions operator having a growth not necessarily of polynomial type. We also give a trace resul
The aim of this paper is to study the regularity of the solutions of problems like (1). The main result is to show that if u is a solution of (1) such that the function w = e µ|u| -1 µ sign(u) belongs to W 1,p 0 (Ω), where µ is some constant, then u is actually Hölder continuous. Then the same resul
In this paper we study the Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = H (x, u, Du)+g (x, u), where the principal term is a Leray-Lions operator defined on W 1,p 0 ( ). Comparison results are obtained between the rearrangement of a solution u of Dirichlet problem