On a weighted trace embedding and applications to critical boundary problems

L. C. F. Ferreira, M. F. Furtado, E. S. Medeiros and J. P. P. da Silva

Mathematische Nachrichten, 2021, vol. 294, issue 5, 877-899

Abstract: We prove a weighted Sobolev trace embedding in the upper half‐space and give its best constant. This embedding can be employed to study a number of critical boundary problems. In this direction, we obtain existence and nonexistence results for a class of semilinear elliptic equations with nonlinear boundary conditions involving critical growth. These equations are closely related to the study of self‐similar solutions for nonlinear reaction‐diffusion equations.

Date: 2021
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