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Maximal $L^2$-regularity
in nonlinear gradient systems and perturbations of sublinear
growth
Wolfgang Arendt and Daniel Hauer |
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Vol. 2 (2020), No. 1, 23–34
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Abstract |
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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. |
Keywords
nonlinear semigroups, subdifferential, Schaefer's fixed
point theorem, existence, smoothing effect, perturbation,
compact sublevel sets
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Mathematical Subject Classification 2010
Primary: 35K92, 35K58, 47H20, 47H10
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Milestones
Received: 14 February 2019
Revised: 3 August 2019
Accepted: 9 September 2019
Published: 9 November 2019
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Authors |
| Wolfgang Arendt | |
| Institute of Applied Analysis University of Ulm Ulm Germany |
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| Daniel Hauer | |
| School of Mathematics and
Statistics The University of Sydney Sydney Australia |
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