A volume constraint problem for the nonlocal doubly nonlinear parabolic equation

Masashi Misawa; Kenta Nakamura; Yoshihiko Yamaura; Masashi Misawa; Kenta Nakamura; Yoshihiko Yamaura

doi:10.3934/mine.2023098

Mathematics in Engineering

2023, Volume 5, Issue 6: 1-26. doi: 10.3934/mine.2023098

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A volume constraint problem for the nonlocal doubly nonlinear parabolic equation

1.
Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan
2.
Headquarters for Admissions and Education, Kumamoto University, Kumamoto 860-8555, Japan
3.
Department of Mathematics, College of Humanities and Sciences, Nihon University, Tokyo 156-8550, Japan

Received: 29 January 2023 Revised: 13 September 2023 Accepted: 14 September 2023 Published: 19 September 2023

We consider a volume constraint problem for the nonlocal doubly nonlinear parabolic equation, called the nonlocal $ p $-Sobolev flow, and introduce a nonlinear intrinsic scaling, converting a prototype nonlocal doubly nonlinear parabolic equation into the nonlocal $ p $-Sobolev flow. This paper is dedicated to Giuseppe Mingione on the occasion of his 50th birthday, who is a maestro in the regularity theory of PDEs.
- nonlocal $ p $-Sobolev flow,
- nonlinear intrinsic scaling,
- doubly nonlinear equations
Citation: Masashi Misawa, Kenta Nakamura, Yoshihiko Yamaura. A volume constraint problem for the nonlocal doubly nonlinear parabolic equation[J]. Mathematics in Engineering, 2023, 5(6): 1-26. doi: 10.3934/mine.2023098

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Abstract

We consider a volume constraint problem for the nonlocal doubly nonlinear parabolic equation, called the nonlocal $ p $-Sobolev flow, and introduce a nonlinear intrinsic scaling, converting a prototype nonlocal doubly nonlinear parabolic equation into the nonlocal $ p $-Sobolev flow. This paper is dedicated to Giuseppe Mingione on the occasion of his 50th birthday, who is a maestro in the regularity theory of PDEs.

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