Proceedings of the American Mathematical Society

Author(s): Marius Mitrea
Journal: Proc. Amer. Math. Soc. 130 (2002), 2599-2607.
MSC (2000): Primary 35B65, 31B10; Secondary 42B20, 46E35
Posted: April 17, 2002
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Abstract: Let

be a second order, (variable coefficient) elliptic differential operator and let $u\in B^{p,p}_\alpha(\Omega)$ , $1<p<\infty$ , $\alpha>0$ , satisfy

in the Lipschitz domain $\Omega$ . We show that

can exhibit more regularity on Besov scales for which smoothness is measured in $L^\tau$ with $\tau<p$ . Similar results are valid for functions representable in terms of layer potentials.

1.: J.Bergh and J.Löfström, Interpolation spaces. An introduction, Springer-Verlag, 1976. MR 58:2349
2.: S.Dahlke and R.A.DeVore, Besov regularity for elliptic boundary value problems, Comm. PDE, Vol.22 (1997), 1-16. MR 97k:35047
3.: S.Dahlke, Besov regularity for second order elliptic boundary value problems with variable coefficients, Manuscripta Math., Vol.95 (1998), 59-77. MR 98m:35038
4.: R.A.DeVore and R.C.Sharpley, Besov spaces on domains in ${\mathbb R}^d$ , Trans. Amer. Math. Soc., Vol.335 (1993), 843-864. MR 93d:46051
5.: M.Frazier and B.Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal., Vol.93 No.1 (1990), 34-170. MR 92a:46042
6.: D.Jerison and C.Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains, J. Funct. Anal., Vol.130 (1995), 161-219. MR 96b:35042
7.: G.Kyriazis, Wavelet coefficients measuring smoothness in $H_p({\mathbb R}^d)$ , Appl. Comput. Harmon. Anal., Vol.3 (1996), 843-864. MR 97h:42016
8.: D. Mitrea, M. Mitrea and M. Taylor, Layer potentials, the Hodge Laplacian and global boundary problems in non-smooth Riemannian manifolds, Memoirs of the Amer. Math. Soc., Vol.150 No.713, Providence RI, 2001. CMP 2001:07
9.: M.Mitrea, Generalized Dirac operators on nonsmooth manifolds and Maxwell's equations, The Journal of Fourier Analysis and Applications, Vol.7 No.3 (2001), 207-256.
10.: M.Mitrea and M.Taylor, Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem, J. Funct. Anal., Vol.176 No.1 (2000), 1-79.
11.: M.Mitrea and M.Taylor, Navier-Stokes equations on Lipschitz domains in Riemannian manifolds, Math. Annalen, Vol.321 (2001), 955-987.
12.: J.Necas, Les Méthodes Directes en Théorie des Équations Élliptiques, Academia, Prague, 1967. MR 37:3168
13.: T.Runst and W.Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Operators, de Gruyter, Berlin, New York, 1996. MR 98a:47071

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35B65, 31B10, 42B20, 46E35

Marius Mitrea
Affiliation: Department of Mathematics, University of Missouri at Columbia, Columbia, Missouri 65211
Email: marius@math.missouri.edu

DOI: 10.1090/S0002-9939-02-06551-6
PII: S 0002-9939(02)06551-6
Keywords: Besov space regularity, Lipschitz domains, layer potentials, smoothness, elliptic PDE
Received by editor(s): March 16, 2001
Posted: April 17, 2002
Additional Notes: The author was partially supported by NSF grant DMS-9870018
Communicated by: Andreas Seeger
Copyright of article: Copyright 2002, American Mathematical Society

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