Existence results for anisotropic and isotropic $p(x)$-Laplace equations

Alkis S. Tersenov

Existence results for anisotropic and isotropic $p(x)$-Laplace equations

Analysis of PDEs 2023-05-10 v1

Authors: Alkis S. Tersenov

Abstract

The Dirichlet problem is considered both for degenerate and singular inhomogeneous quasilinear parabolic equations. We prove the existence of a solution $u$ such that $u_t$ belongs to $L_{\infty}$ . The $L_{\infty}$ estimate of $u_t$ is obtained by introducing a new time variable.

Keywords

Dirichlet problem p(x)-Laplace equation quasilinear parabolic equations existence of solution L-infinity estimate

Cite

@article{arxiv.2305.05437,
  title  = {Existence results for anisotropic and isotropic $p(x)$-Laplace equations},
  author = {Alkis S. Tersenov},
  journal= {arXiv preprint arXiv:2305.05437},
  year   = {2023}
}

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