On Well-Posedness of the Nonlocal Boundary Value Problems for Elliptic Equations

Abstract

The nonlocal boundary value problem

in an arbitrary Banach space E with the positive operator A is considered. The well-posedness of this boundary value problem in the spaces of smooth functions is established. The new exact Schauder's estimates of solutions of the boundary value problems for elliptic equations are obtained.

Keywords:

• Sobolevskii's coercive inequality
• Elliptic equation
• Nonlocal boundary value problems
• Exact Schauder's estimates
• 1991 Mathematics Subject Classification: 35J
• 65N

Acknowledgment

The author is grateful to Muhammet Meredov, Prof. of Department of Applied Mathematics of International Turkmen-Turkish University (Ashgabat, Turkmenistan), Member of AS of Turkmenistan and to Pavel Sobolevskii, Prof. of Institute of Mathematics of Hebrew University (Jerusalem, Israel) for valuable suggestions.