Neumann problem and one oblique-derivative problem for an improperly elliptic equation
- 49 Downloads
We study the problem of solvability of an inhomogeneous Neumann problem and an oblique-derivative problem for an improperly elliptic scalar differential equation with complex coefficients in a bounded domain. A model case in which the domain is a unit disk and the equation does not contain lower-order terms is investigated. It is shown that the classes of boundary data for which these problems are uniquely solvable in a Sobolev space are formed by the spaces of functions with exponentially decreasing Fourier coefficients.
KeywordsElliptic Equation Unit Disk Dirichlet Problem Neumann Problem Pseudodifferential Operator
Unable to display preview. Download preview PDF.
- 2.A. V. Bitsadze, Some Classes of Partial Differential Equations [in Russian], Nauka, Moscow (1981).Google Scholar
- 6.V. P. Burskii, Methods for Investigation of Boundary-Value Problems for General Differential Equations [in Russian], Naukova Dumka, Kiev (2002).Google Scholar
- 8.Yu. V. Egorov and V. A. Kondrat’ev, “On the oblique-derivative problem,” Mat. Sb., 78 (120), 148–176 (1969).Google Scholar
- 9.Yu. V. Egorov and M. A. Shubin, “Linear partial differential equations. Foundations of the classical theory,” in: VINITI Series in Contemporary Problems of Mathematics, Fundamental Trends [in Russian], Vol. 30, VINITI, Moscow (1987), pp. 1–264.Google Scholar
- 13.S. Mandelbrojt, Quasianalytic Classes of Functions [Russian translation], ONTI NKTR SSSR, Leningrad (1937).Google Scholar
- 14.L. Hörmander, The Analysis of Linear Partial Differential Operators. Vol. 3. Pseudo-Differential Operators [Russian translation], Mir, Moscow (1967), pp. 166–297.Google Scholar