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) (KAR id:31253)

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

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

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

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

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:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Ian Wood
Date Deposited:	04 Oct 2012 10:32 UTC
Last Modified:	16 Feb 2021 12:42 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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