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http://hdl.handle.net/10773/15597
Title: | Quasilinear elliptic systems with measure data |
Author: | Leonetti, Francesco Rocha, Eugénio Staicu, Vasile |
Keywords: | Elliptic systems Existence of solutions Measures |
Issue Date: | May-2016 |
Publisher: | Elsevier |
Abstract: | We study the existence of solutions of quasilinear elliptic systems involving $N$ equations and a measure on the right hand side, with the form $$\left\{\begin{array}{ll} -\sum_{i=1}^n \frac{\partial}{\partial x_i}\left(\sum\limits_{\beta=1}^{N}\sum\limits_{j=1}^{n}% a_{i,j}^{\alpha,\beta}\left( x,u\right)\frac{\partial}{\partial x_j}u^\beta\right)=\mu^\alpha& \mbox{ in }\Omega ,\\ u=0 & \mbox{ on }\partial\Omega, \end{array}\right.$$ where $\alpha\in\{1,\dots,N\}$ is the equation index, $\Omega$ is an open bounded subset of $\mathbb{R}^{n}$, $u:\Omega\rightarrow\mathbb{R}^{N}$ and $\mu$ is a finite Randon measure on $\mathbb{R}^{n}$ with values into $\mathbb{R}^{N}$. Existence of a solution is proved for two different sets of assumptions on $A$. Examples are provided that satisfy our conditions, but do not satisfy conditions required on previous works on this matter. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/15597 |
DOI: | 10.1016/j.na.2016.04.002 |
ISSN: | 0362-546X |
Appears in Collections: | CIDMA - Artigos FAAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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LRSPaper_online.pdf | main | 720.34 kB | Adobe PDF |
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