The solvability of the Dirichlet problem for quasilinear elliptic second-order equations of nondivergence form are studied in a domain whose boundary contains a conical point or an edge of an arbitrary codimension. Bibliography: 12 titles.
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V. G. Maz'ya and B. A. Plamenevskii, “L p-estimates for solutions to elliptic boundary-value problems in domains with edges,” Tr. Mosk. Mat. O.va [in Russian], 37, 49–93 (1978).
V. G. Maz'ya and B. A. Plamenevskii, “Estimates in L p and in Hölder classes, and the Miranda-Agmon maximum principle for the solutions of elliptic boundary-value problems in domains with singular points on the boundary,” Math. Nachr., 81, 25–82 (1978).
V. Maz'ya and J. Rossman, “On the Agmon-Miranda maximum principle for solutions of elliptic equations in polihedral and polygonal domains,” Ann. Global Anal. Geom., 9, No. 3, 253–303 (1991).
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Apushkinskaya, D.I., Nazarov, A.I. The Dirichlet Problem for Quasilinear Elliptic Equations in Domains with Smooth Closed Edges. Journal of Mathematical Sciences 105, 2299–2318 (2001). https://doi.org/10.1023/A:1011362311390
- Elliptic Equation
- Dirichlet Problem
- Conical Point
- Quasilinear Elliptic Equation
- Closed Edge