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Maximal L^p -regularity for the Laplacian on Lipschitz domains

Wood, Ian (2007) Maximal L^p -regularity for the Laplacian on Lipschitz domains. Mathematische Zeitschrift, 255 (4). pp. 855-875. ISSN 0025-5874. (doi:10.1007/s00209-006-0055-6) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1007/s00209-006-0055-6

Abstract

We consider the Laplacian with Dirichlet or Neumann boundary

conditions on bounded Lipschitz domains ?, both with the following two domains of

definition:D1(?) = {u ? W1,p(?) : ?u ? Lp(?), Bu = 0}, orD2(?) = {u ? W2,p(?) :

Bu = 0}, where B is the boundary operator.We prove that, under certain restrictions

on the range of p, these operators generate positive analytic contraction semigroups

on Lp(?) which implies maximal regularity for the corresponding Cauchy problems.

In particular, if ? is bounded and convex and 1 < p ? 2, the Laplacian with domain

D2(?) has the maximal regularity property, as in the case of smooth domains. In the

last part,we construct an example that proves that, in general, the Dirichlet–Laplacian

with domain D1(?) is not even a closed operator.

Item Type: Article
DOI/Identification number: 10.1007/s00209-006-0055-6
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 04 Oct 2012 10:32 UTC
Last Modified: 01 Aug 2019 10:35 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/31253 (The current URI for this page, for reference purposes)
Wood, Ian: https://orcid.org/0000-0001-7181-7075
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