Existence for evolutionary problems with linear growth by stability methods

Bögelein V, Duzaar F, Schätzler L, Scheven C (2019)

Publication Language: English

Publication Type: Journal article

Publication year: 2019

Journal

Journal of Differential Equations Elsevier

Book Volume: 266

Pages Range: 7709-7748

Journal Issue: 11

DOI: 10.1016/j.jde.2018.12.012

Abstract

We establish that solutions to the Cauchy–Dirichlet problem for functionals f:_ ×RN×n→[0, ∞)of linear growth can be obtained as limits of solutions to flows with p-growth in the limit p↓1. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.∂tu −div _Dξf (x,Du)_ = 0

Authors with CRIS profile

Verena Anna Maria Bögelein
Frank Duzaar Lehrstuhl für Partial Differential Equations Leah Schätzler

Involved external institutions

Universität Salzburg (Paris Lodron Universität Salzburg) AT Austria (AT) Universität Duisburg-Essen (UDE) DE Germany (DE)

How to cite

APA:

Bögelein, V., Duzaar, F., Schätzler, L., & Scheven, C. (2019). Existence for evolutionary problems with linear growth by stability methods. Journal of Differential Equations, 266(11), 7709-7748. https://dx.doi.org/10.1016/j.jde.2018.12.012

MLA:

Bögelein, Verena, et al. "Existence for evolutionary problems with linear growth by stability methods." Journal of Differential Equations 266.11 (2019): 7709-7748.

BibTeX: Download