Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications. (English) Zbl 07920510
Summary: 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.
MSC:
| 35J20 | Variational methods for second-order elliptic equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35J50 | Variational methods for elliptic systems |
Keywords:
Sobolev spaces; Trudinger-Moser inequality; Adams inequality; differential equations; fractional dimensions; extremals; sharp constantReferences:
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