Abstract
We prove trace theorems for weighted, mixed-norm, Sobolev spaces in the upper-half space where the weight is a power function of the vertical variable. The results show the differentiability order of the trace functions depends only on the power in the weight function and the integrability power for the integration with respect to the vertical variable but not on the integrability powers for the integration with respect to the horizontal ones. They recover classical results in the case of unmixed-norm spaces. The work is motivated by the study of regularity theory for solutions of elliptic and parabolic equations with anisotropic features and with nonhomogeneous boundary conditions. The results provide an essential ingredient to the study of fractional elliptic and parabolic equations in divergence form with measurable coefficients.
Published Version
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