Maslennikova, V. N.; Bogovskij, M. E. Elliptic boundary value problems in unbounded domains with noncompact and nonsmooth boundaries. (English) Zbl 0659.35030 Rend. Semin. Mat. Fis. Milano 56, 125-138 (1986). This note studies the solvability and uniqueness in \(L_ p\) \((1<p<+\infty)\) of solutions of Dirichlet and Neumann problems for linear second order uniformly elliptic equations (of non-divergence type), in unbounded domains with nonsmooth and noncompact boundaries. Reviewer: M.Chicco Cited in 28 Documents MSC: 35J25 Boundary value problems for second-order elliptic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:solvability; uniqueness; Dirichlet; Neumann problems; uniformly elliptic; non-divergence type; unbounded domains; nonsmooth and noncompact boundaries PDFBibTeX XMLCite \textit{V. N. Maslennikova} and \textit{M. E. Bogovskij}, Rend. Semin. Mat. Fis. Milano 56, 125--138 (1986; Zbl 0659.35030) Full Text: DOI References: [1] Kondrat’ev, V. A.; Oleinik, O. A., Boundary-value problems for partial differential equations in non-smooth domains, Russian Mathematical Surveys (London Math. Soc.), 38, 1-86 (1983) · Zbl 0548.35018 · doi:10.1070/RM1983v038n02ABEH003470 [2] Mazja, V. G.; Plamenevskii, B. A., Estimates in L^pand in the Hölder classes and Miranda-Agmon’s principle for the solvability of elliptic boundary value problems in domains with irregular points on the boundary, (Russian), Math. Nachr., 81, 25-82 (1978) · Zbl 0371.35018 · doi:10.1002/mana.19780810103 [3] Bogovskiî, M. E., Decomposition of L^p (Ω: ℝ^n)into a direct sum of subspaces connected with solenoidal and potential vector fields. (Russian), Dokl. Akad. Nauk. S.S.S.R., 286, 781-786 (1986) [4] Heywood, J. G., On uniqueness questions in the theory of viscous flow, Acta Math., 136, 61-102 (1976) · Zbl 0347.76016 · doi:10.1007/BF02392043 [5] Bogovskiî, M. E., On the L_p-theory of the Navier-Stokes system for unbounded domain with noncompact boundaries, Soviet Math. Dokl., 22, 809-814 (1980) · Zbl 0465.35077 [6] Maslennikova V. N. andBogovskiî M. E.,Approximation of solenoidal and potential vector fields in Sobolev spaces and problems of Mathematical Physics. (Russian) contained in the book:Partial Differential Equations Nauka, Novosibirsk (1986), p. 129-137. · Zbl 0629.35027 [7] Grisvard P.,Elliptic problems in nonsmooth domains, Boston-London-Melbourne, Pitman Advanced Publications Program, 1985, 410 p. · Zbl 0695.35060 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.