Abstract
We consider here a class of anisotropic elliptic equations, in a bounded domain $\Omega$ with Lipschitz continuous boundary $\partial \Omega$, of the type $$ -\sum_{i=1}^{N}\partial_{x_{i}}\big(a_{i}(x,u) |\partial_{x_{i}}u|^{p_{i}-2}\partial_{x_{i}} u\big) =f- {\rm div} g $$ with Dirichlet boundary conditions. Using the framework of renormalized solutions we prove the uniqueness of the solution under a very local Lipschitz condition on the coefficients $a_{i}(x,s)$ with respect to $s$ and with $f$ belonging to $L^1(\Omega)$.
Citation
Rosaria Di Nardo. Filomena Feo. Olivier Guibé. "Uniqueness result for nonlinear anisotropic elliptic equations." Adv. Differential Equations 18 (5/6) 433 - 458, May/June 2013. https://doi.org/10.57262/ade/1363266253
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