Existence for doubly nonlinear fractional $p$-Laplacian equations

Nobuyuki Kato; Masashi Misawa; Kenta Nakamura; Yoshihiko Yamaura

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arXiv · 2305.00661

Existence for doubly nonlinear fractional $p$-Laplacian equations

Nobuyuki Kato·Masashi Misawa·Kenta Nakamura·Yoshihiko Yamaura

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Abstract

In this paper we prove the existence of a weak solution to a doubly nonlinear parabolic fractional $p$-Laplacian equation, which has general doubly non-linearlity including not only the Sobolev subcritical/critical/supercritical cases but also the slow/fast diffusion ones. Our proof reveals the weak convergence method for the doubly nonlinear fractional $p$-Laplace operator.

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Nobuyuki Kato, Masashi Misawa, Kenta Nakamura, Yoshihiko Yamaura. 2023-05-01. Existence for doubly nonlinear fractional $p$-Laplacian equations. https://arxiv.org/abs/2305.00661

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