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arXiv · 2308.05643

On solvability in the small of higher order elliptic equations in Orlicz-Sobolev spaces

Javad A. Asadzade
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Abstract

In this article, we consider a higher-order elliptic equation with nonsmooth coefficients with respect to Orlicz spaces on the domain $\Omega\subset\mathbb{R}^{n}$. The separable subspace of this space is distinguished in which infinitely differentiable and compactly supported functions are dense; Sobolev spaces generated by these subspaces are determined. We demonstrate the local solvability of the equation in Orlicz-Sobolev spaces under specific restrictions on the coefficients of the equation and the Boyd indices of the Orlicz space. This result strengthens the previously known classical $L_{p}$ analog.

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Javad A. Asadzade. 2023-08-10. On solvability in the small of higher order elliptic equations in Orlicz-Sobolev spaces. https://arxiv.org/abs/2308.05643

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