Translator Disclaimer
2020 Maximal $L^2$-regularity in nonlinear gradient systems and perturbations of sublinear growth
Wolfgang Arendt, Daniel Hauer
Pure Appl. Anal. 2(1): 23-34 (2020). DOI: 10.2140/paa.2020.2.23

Abstract

The nonlinear semigroup generated by the subdifferential of a convex lower semicontinuous function φ has a smoothing effect, discovered by Haïm Brezis, which implies maximal regularity for the evolution equation. We use this and Schaefer’s fixed point theorem to solve the evolution equation perturbed by a Nemytskii operator of sublinear growth. For this, we need that the sublevel sets of φ are not only closed, but even compact. We apply our results to the p-Laplacian and also to the Dirichlet-to-Neumann operator with respect to p-harmonic functions.

Citation

Download Citation

Wolfgang Arendt. Daniel Hauer. "Maximal $L^2$-regularity in nonlinear gradient systems and perturbations of sublinear growth." Pure Appl. Anal. 2 (1) 23 - 34, 2020. https://doi.org/10.2140/paa.2020.2.23

Information

Received: 14 February 2019; Revised: 3 August 2019; Accepted: 9 September 2019; Published: 2020
First available in Project Euclid: 13 December 2019

zbMATH: 07159295
MathSciNet: MR4041276
Digital Object Identifier: 10.2140/paa.2020.2.23

Subjects:
Primary: 35K58 , 35K92 , 47H10 , 47H20

Keywords: compact sublevel sets , existence , nonlinear semigroups , perturbation , Schaefer's fixed point theorem , Smoothing effect , subdifferential

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.2 • No. 1 • 2020
MSP
Back to Top