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Title: Quasilinear elliptic systems with measure data
Author: Leonetti, Francesco
Rocha, Eugénio
Staicu, Vasile
Keywords: Elliptic systems
Existence of solutions
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
DOI: 10.1016/
ISSN: 0362-546X
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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