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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… Click to show full 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.
Keywords:
embedding applications;
trace embedding;
weighted trace;
critical boundary;
boundary problems
Journal Title: Mathematische Nachrichten
Year Published: 2021
Link to full text (if available)
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Journal Title: Mathematische Nachrichten
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!