In the present book we study solvability and uniqueness of the soution to the Dirichlet problem for the p-Laplace equation and the equation of Helmholtz type. For the functions in Sobolev spaces of first order their boundary traces are characterized for the interior and exterior of the multidimensional paraboloid. Thus, necessary and sufficient conditions are obtained for solvability of the above Dirichlet problem inside and outside the paraboloid. The monograph is addressed to the students of higher courses and PhD students whose scientific interests lie in the function theory and the theory of boundary value problems for partial differential equations.

Graduated from the Mathematical and Mechanical Department of Leningrad State University in 1971. Candidate of science(PhD) since 1981. Doctor of science since 2001. Profesor of Petersburg State University since 2002.Scientific interests: Sobolev spaces and their applications to partial differential equations