The Dirichlet Problem for Harmonic Functions in the Smirnov Class with Variable Exponent
Vakhtang Mikhailovich Kokilashvili, Vakhtang Paatashvili · Georgian Mathematical Journal · 2007
Abstract A solution of the Dirichlet problem for harmonic functions from the Smirnov class is obtained in the framework of functional spaces with a nonstandard growth condition. It is found that the domain boundary geometry influences the character of a problem solution. In the case of solvability, solutions are constructed in explicit form.