Geodesic
To the Theory of the Dirichlet and Neumann Problems for Strongly Elliptic Systems in Lipschitz Domains
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 1-21

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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.
Keywords: strong ellipticity, Lipschitz domain, Dirichlet problem, Neumann problem, potential space, Whitney array.
Mots-clés : variational solution, Besov space 
@article{FAA_2007_41_4_a0,
     author = {M. S. Agranovich},
     title = {To the {Theory} of the {Dirichlet} and {Neumann} {Problems} for {Strongly} {Elliptic} {Systems} in {Lipschitz} {Domains}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {1--21},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a0/}
}
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M. S. Agranovich. To the Theory of the Dirichlet and Neumann Problems for Strongly Elliptic Systems in Lipschitz Domains. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 1-21. http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a0/