|
|||||
 |
|
|
|
|
|
|
Maximal $L^2$-regularity
in nonlinear gradient systems and perturbations of sublinear
growth
Wolfgang Arendt and Daniel Hauer |
|
Vol. 2 (2020), No. 1, 23–34
|
Abstract |
|
The nonlinear semigroup generated by the subdifferential of a convex lower semicontinuous function 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 are not only closed, but even compact. We apply our results to the -Laplacian and also to the Dirichlet-to-Neumann operator with respect to -harmonic functions. |
PDF Access Denied
We have not been able to recognize your IP address
3.145.186.173
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
nonlinear semigroups, subdifferential, Schaefer's fixed
point theorem, existence, smoothing effect, perturbation,
compact sublevel sets
|
Mathematical Subject Classification 2010
Primary: 35K92, 35K58, 47H20, 47H10
|
Milestones
Received: 14 February 2019
Revised: 3 August 2019
Accepted: 9 September 2019
Published: 9 November 2019
|
Authors |
| Wolfgang Arendt | |
| Institute of Applied Analysis University of Ulm Ulm Germany |
|
| Daniel Hauer | |
| School of Mathematics and
Statistics The University of Sydney Sydney Australia |
|
