Geodesic
Mixed Problems in a Lipschitz Domain for Strongly Elliptic Second-Order Systems
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 2, pp. 1-22

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We consider mixed problems for strongly elliptic second-order systems in a bounded domain with Lipschitz boundary in the space $\mathbb{R}^n$. For such problems, equivalent equations on the boundary in the simplest $L_2$-spaces $H^s$ of Sobolev type are derived, which permits one to represent the solutions via surface potentials. We prove a result on the regularity of solutions in the slightly more general spaces $H^s_p$ of Bessel potentials and Besov spaces $B^s_p$. Problems with spectral parameter in the system or in the condition on a part of the boundary are considered, and the spectral properties of the corresponding operators, including the eigenvalue asymptotics, are discussed.
Keywords: strongly elliptic system, mixed problem, potential type operator, spectral problem, eigenvalue asymptotics. 
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     author = {M. S. Agranovich},
     title = {Mixed {Problems} in a {Lipschitz} {Domain} for {Strongly} {Elliptic} {Second-Order} {Systems}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {1--22},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_2_a0/}
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M. S. Agranovich. Mixed Problems in a Lipschitz Domain for Strongly Elliptic Second-Order Systems. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 2, pp. 1-22. http://geodesic.mathdoc.fr/item/FAA_2011_45_2_a0/