Back to Search
Start Over
Remarks on some quasilinear equations with gradient terms and measure data
- Source :
- CONTEMPORARY MATHEMATICS-AMERICAN MATHEMATICAL SOCIETY, Artículos CONICYT, CONICYT Chile, instacron:CONICYT
- Publication Year :
- 2012
-
Abstract
- Let $\Omega \subset \mathbb{R}^{N}$ be a smooth bounded domain, $H$ a Caratheodory function defined in $\Omega \times \mathbb{R\times R}^{N},$ and $\mu $ a bounded Radon measure in $\Omega .$ We study the problem% \begin{equation*} -\Delta_{p}u+H(x,u,\nabla u)=\mu \quad \text{in}\Omega,\qquad u=0\quad \text{on}\partial \Omega, \end{equation*} where $\Delta_{p}$ is the $p$-Laplacian ($p>1$)$,$ and we emphasize the case $H(x,u,\nabla u)=\pm \left\| \nabla u\right\| ^{q}$ ($q>0$). We obtain an existence result under subcritical growth assumptions on $H,$ we give necessary conditions of existence in terms of capacity properties, and we prove removability results of eventual singularities. In the supercritical case, when $\mu \geqq 0$ and $H$ is an absorption term, i.e. $% H\geqq 0,$ we give two sufficient conditions for existence of a nonnegative solution.<br />Comment: To appear in Contemporary Mathematics
- Subjects :
- Bessel capacity
removable set
010102 general mathematics
35J92, 35J62, 31A15
Mathematics::Analysis of PDEs
renormalized solutions
measure
16. Peace & justice
01 natural sciences
010101 applied mathematics
Mathematics - Analysis of PDEs
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
p-Laplace
0101 mathematics
Analysis of PDEs (math.AP)
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- CONTEMPORARY MATHEMATICS-AMERICAN MATHEMATICAL SOCIETY, Artículos CONICYT, CONICYT Chile, instacron:CONICYT
- Accession number :
- edsair.doi.dedup.....b2dcc9be02e44ec6b5b9571899efb8fa