Elliptic Equations Boundary Data Disturbances

This dissertation studies the effect of the perturbation of the boundary data on the solution of elliptic equations. We first analyze the cases for the elliptic equations with constant or variable coefficients in the half-space IR+n·When the distance from the part of the boundary, where the data is perturbed, goes to infinity, the perturbation of the solution will decay with n-1 power of the distance. Later, we discuss the case in a bounded domain and find that the perturbation will also decay with n-1 power of the distance if the domain is large enough. Finally, we apply our results to study the Tricomi problem of the Lavrentiev-Bitsadze equation.