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arXiv · 1912.12432

On solutions of elliptic equations with variable exponents and measure data in $\mathbb{R}^n$

L. M. Kozhevnikova
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Abstract

Anisotropic elliptic equations of the second order with variable exponents in nonlinearities and the right-hand side as a diffuse measure are considered in the space $\mathbb{R}^n$. The existence of an entropy solution in anisotropic Sobolev--Orlicz spaces with variable exponents is proved. The obtained entropy solution is shown to be a renormalized solution.

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L. M. Kozhevnikova. 2019-12-28. On solutions of elliptic equations with variable exponents and measure data in $\mathbb{R}^n$. https://arxiv.org/abs/1912.12432

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