Abstract
We consider the minimization of a functional of the calculus of variations, under assumptions that are diffeomorphism invariant. In particular, a nonuniform coercivity condition needs to be considered. We show that the direct methods of the calculus of variations can be applied in a generalized Sobolev space, which is in turn diffeomorphism invariant. Under a suitable (invariant) assumption, the minima in this larger space belong to a usual Sobolev space and are bounded.
| Original language | English |
|---|---|
| Pages (from-to) | 1-23 |
| Number of pages | 23 |
| Journal | Mathematics |
| Volume | 13 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2025 |
All Science Journal Classification (ASJC) codes
- Computer Science (miscellaneous)
- General Mathematics
- Engineering (miscellaneous)
Keywords
- Calculus of variations
- Direct methods
- Invariance by diffeomorphism
- Quasilinear elliptic equations
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