Invertibility of some heat potentials in BMO norms
type: Item
instance of: scholarly article
title: Invertibility of some heat potentials in BMO norms
zbMATH Open document ID: 0615.35007
author: Francesco Ragnedda
author: Umberto Neri
author: Anna Piro Grimaldi
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108032
review text: For \(C^ 1\) domains D in \(R^ n\) and \(L^ p\) boundary data the initial-Dirichlet problem \(\Delta_ xu-D_ t=0\) in the cylinder \(D\times (0,T),\lim_{t\to 0} u(X,t)=0\) uniformly on compacts in D, u(X,t)\(\to f(P,s)\) on the lateral surface \(\partial D\times (0,T)\), is analyzed. Continuity of the boundary integral \([Jf](P,t)=\lim_{\epsilon \to 0} \iint^{t-\epsilon}_{\partial D}K(P,Q,t-s)dQ ds\)where K is the corresponding kernel of the double-layer heat potential, was proved in the two first authors' previous work [ibid. 72, 289-305 (1984; Zbl 0561.35037)]. In the present paper the invertibility of the boundary terms \(cI+J\), \(c\neq 0\) and I-identity operator, in \(B_ 0 MOC(\partial D\times (0,T))\) is established, where \(B_ 0 MOC\) is a subspace of functions f with caloric bounded mean oscillation (BMOC) having bounded initial behaviour at \(t=0\).
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 3996199
zbMATH Keywords: L\({}^ p\) boundary data
zbMATH Keywords: initial-Dirichlet problem
zbMATH Keywords: double-layer heat potential
zbMATH Keywords: invertibility
zbMATH Keywords: caloric bounded mean oscillation
MaRDI profile type: Publication
cites work: Q3876328
cites work: Systems of parabolic equations with uniformly continuous coefficients
cites work: Q3882733
cites work: BMO continuity for some heat potentials
description: scientific article; zbMATH DE number 3996199