Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications
Analysis of PDEs
2024-10-24 v1
Abstract
We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths admit nontrivial solutions.
Keywords
Cite
@article{arxiv.2302.02262,
title = {Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications},
author = {João Marcos do Ó and Guozhen Lu and Raoní Ponciano},
journal= {arXiv preprint arXiv:2302.02262},
year = {2024}
}