A parabolic bipolynomial fractional Dirichlet-Laplace problem

[摘要] We derive existence results for a parabolic bipolynomial abstract and classical problems containing fractional powers of the Dirichlet-Laplace operator on a bounded domain, in the sense of the Stone-von Neumann operator calculus. The main tools are theorems on the existence and uniqueness of a weak solutions to an abstract problem, due to Friedman, and a general theorem on the equivalence of weak and strong solutions to some operator equation.

[学科分类] 数学（综合）

[关键词] Parabolic equation;fractional Dirichlet-Laplace operator;existence of solutions.