A direct proof of existence of weak solutions to elliptic problems
DOI:
https://doi.org/10.12775/TMNA.2023.019Keywords
xistence, elliptic boundary value problems, second order partial differential equations, Musielak-Orlicz spacesAbstract
We provide a direct proof of existence and uniqueness of weak solutions to a broad family of strongly nonlinear elliptic equations with lower-order terms. The leading part of the operator satisfies general growth conditions settling the problem in the framework of fully anisotropic and inhomogeneous Musielak-Orlicz spaces generated by an $N$-function \linebreak $M\colon \Omega\times\mathbb R^d\to [0,\infty)$. Neither $\nabla_2$ nor $\Delta_2$ conditions are imposed on $M$. Our results cover among others problems with anisotropic polynomial, Orlicz, variable exponent, and double phase growth.References
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Copyright (c) 2023 Iwona Chlebicka, Arttu Karppinen, Ying Li
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