To the Theory of the Dirichlet and Neumann Problems for Strongly Elliptic Systems in Lipschitz Domains

M. S. Agranovich

Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 1-21.

Résumé

For strongly elliptic systems with Douglis–Nirenberg structure, we investigate the regularity of variational solutions to the Dirichlet and Neumann problems in a bounded Lipschitz domain. The solutions of the problems with homogeneous boundary conditions are originally defined in the simplest $L_2$-Sobolev spaces $H^\sigma$. The regularity results are obtained in the potential spaces $H^\sigma_p$ and Besov spaces $B^\sigma_p$. In the case of second-order systems, the author's results obtained a year ago are strengthened. The Dirichlet problem with nonhomogeneous boundary conditions is considered using Whitney arrays.

Détail

Keywords: strong ellipticity, Lipschitz domain, Dirichlet problem, Neumann problem, potential space, Whitney array.
Mots-clés : variational solution, Besov space

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