SMS scnews item created by Sanjana Bhardwaj at Thu 11 May 2023 1736
Type: Seminar
Modified: Thu 11 May 2023 2111
Distribution: World
Expiry: 22 May 2023
Calendar1: 22 May 2023 1500-1600
CalLoc1: Zoom webinar
CalTitle1: Continuity of a spatial derivative for a perturbed one-Laplace equation
Auth: sanjana@sanjana.staff.wireless.sydney.edu.au (sbha9594) in SMS-SAML

Asia-Pacific Analysis and PDE Seminar

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

Shuntaro Tsubouchi

Dear friends and colleagues,   
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

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. .

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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Webinar Speaker

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 .