Parabolic systems with polynomial growth and regularity

Duzaar F, Mingione G, Steffen K (2011)

Publication Type: Journal article

Publication year: 2011

Journal

Memoirs of the American Mathematical Society American Mathematical Society

Publisher: American Mathematical Society

Book Volume: 214

Pages Range: -

Journal Issue: 1005

URI: http://www.ams.org/journals/memo/0000-000-00/S0065-9266-2011-00614-3/home.html

DOI: 10.1090/S0065-9266-2011-00614-3

Abstract

We establish a series of optimal regularity results for solutions to general nonlinear parabolic systems u t - div a(x, t, u, Du) + H = 0, under the main assumption of polynomial growth at rate p i.e. |a(x, t, u, Du)| ≤ L(1 + |Du| ^p-1), p ≥ 2. We give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderón-Zygmund estimates for non-homogeneous problems are here achieved.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

Heinrich-Heine-Universität Düsseldorf

Germany (DE) University of Parma / Università degli Studi di Parma

Italy (IT)

How to cite

APA:

Duzaar, F., Mingione, G., & Steffen, K. (2011). Parabolic systems with polynomial growth and regularity. Memoirs of the American Mathematical Society, 214(1005), -. https://doi.org/10.1090/S0065-9266-2011-00614-3

MLA:

Duzaar, Frank, Giuseppe Mingione, and Klaus Steffen. "Parabolic systems with polynomial growth and regularity." Memoirs of the American Mathematical Society 214.1005 (2011): -.

BibTeX: Download