2. VARIATIONAL DIRICHLET PROBLEM FOR ELLIPTIC OPERATORS IN THE WHOLE SPACE WITH UNCOORDINATED DEGENERACY OF COEFFICIENTS
Author: SULAIMON ISKHOKOV AND BAKHTOVAR RAKHMONOV DOWNLOAD
DOI:
Abstract
In paper we investigate solvability of the variational Dirichlet problem for a class of elliptic differential operators in the whole space. The sesquilinear form associated with the operator under study is represented as a finite sum of auxiliary sesquilinear forms and the concept of ¡¡leading form¿¿ is introduced. Depending on the behavior of the coefficients of the leading forms, the main weighted space of differentiable functions of many real variables in the entire space is introduced. The solvability of the variational Dirichlet problem is studied in this space.
Keywords
elliptic differential operator, variational Dirichlet problem, whole space, uncoordinated degeneracy,noncoercive sesquilinear form.