Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0615.35007
Grimaldi-Piro, Anna; Ragnedda, Francesco; Neri, Umberto
Invertibility of some heat potentials in BMO norms. (English)
[J] Rend. Semin. Mat. Univ. Padova 75, 77-90 (1986). ISSN 0041-8994

For $C\sp 1$ domains D in $R\sp n$ and $L\sp p$ boundary data the initial-Dirichlet problem $\Delta\sb xu-D\sb t=0$ in the cylinder $D\times (0,T),\lim\sb{t\to 0} u(X,t)=0$ 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 $[Jf](P,t)=\lim\sb{\epsilon \to 0} \iint\sp{t-\epsilon}\sb{\partial D}K(P,Q,t-s)dQ ds$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)]. \par In the present paper the invertibility of the boundary terms $cI+J$, $c\ne 0$ and I-identity operator, in $B\sb 0 MOC(\partial D\times (0,T))$ is established, where $B\sb 0 MOC$ is a subspace of functions f with caloric bounded mean oscillation (BMOC) having bounded initial behaviour at $t=0$.
[J.Zino]

MSC 2000:: *35B65 Smoothness of solutions of PDE
35K20 Second order parabolic equations, boundary value problems
35K05 Heat equation

Keywords: L${}\sp p$ boundary data; initial-Dirichlet problem; double-layer heat potential; invertibility; caloric bounded mean oscillation

Citations: Zbl 0561.35037

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]