Type: Seminar

Modified: Thu 11 May 2023 2111

Distribution: World

Expiry: 22 May 2023

CalTitle1: Continuity of a spatial derivative for a perturbed one-Laplace equation

Auth: sanjana@sanjana.staff.wireless.sydney.edu.au (sbha9594) in SMS-SAML

Dear friends and colleagues,
## Webinar Speaker

on **Monday, 22 May 2023** at

•**1 PM** for Beijing, Hong Kong and Perth

•**2 PM** for Seoul and Tokyo

•**3 PM** for Canberra, Melbourne and Sydney

•**5 PM** for Auckland

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PhD. Candidate ** Shuntaro Tsubouchi ** is giving a talk in our Asia-Pacific Analysis and PDE Seminar on

Continuity of a spatial derivative for a perturbed one-Laplace equation spaces

**Abstract:**

This talk is concerned with continuity of a spatial derivative for a weak solution to a one-Laplace elliptic equation perturbed by the $p$-Laplace operator with $p\in(1,\,\infty)$. The main difficulty herein is that the one-Laplace operator has both singular and degenerate ellipticity. Due to this anisotropic diffusivity, the equation becomes no longer uniformly elliptic near a facet, the place where a gradient degenerates. Since the one-Laplace operator seems difficult to handle in existing regularity theory, continuity of a spatial gradient has been a long-standing open problem. Recently, the lecturer, inspired by a regularity result on a very degenerate elliptic problem, has found it possible to prove continuous differentiability of a weak solution. The aim of this talk is to explain how continuity of a spatial gradient is shown.
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**Chair:** Yoshikazu Giga (Professor @ University of Tokyo)

More information and how to attend this talk can be found at the seminar webpage

Sanjana

On behalf of Daniel H. and Ben

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Shuntaro Tsubouchi

PhD Candidate@ University of Tokyo, Japan

Shuntaro Tsubouchi is a Ph.D. candidate in the Graduate School of Mathematical Sciences at the University of Tokyo. He received a master's degree in 2021 under the supervision of Professor Yoshikazu Giga at the University of Tokyo, and is currently supervised by Professor Kazuhiro Ishige at the University of Tokyo. His research interests are in regularity theory for anisotropic elliptic/parabolic PDE, and in particular, he is currently studying continuity of spatial gradients for some very singular problems involving a one-Laplace-type operator .

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