Dirichlet Boundary Value Problems For The Perturbation Of Spectral Fractional Laplacian By A Gradient Operator

In this paper,we use the method of analysis to prove that there exists a unique weak solutio to the following boundary value equation:Au=(?)_tu+(?|_D)^?/2u+(?)u·?,?(1,2),The drift term of operator is a signed measure that satisfies a specific kato class.Since we know the solution of the equation is known when the drift term is a function that meets a specific kato class and the definition of the solution,We mainly use the method of smooth function approximation to prove the existence of the above equations.The main tools used in this paper are that Dirichlet heat kernel estimate,Duhamel's formula and the definition of the Kato class.