Compactness properties and ground states for the affine Laplacian. (English) Zbl 1436.46042
The paper under review studies compactness properties of the affine Sobolev inequality of E. Lutwak et al. [J. Differ. Geom. 62, No. 1, 17–38 (2002; Zbl 1073.46027)] and G.-Y. Zhang [J. Differ. Geom. 53, No. 1, 183–202 (1999; Zbl 1040.53089)] in the case \(p = 2\), and the existence and regularity of related minimizers, in particular, solutions to nonlocal Dirichlet problems.
Reviewer: Youssef El Hadfi (Khouribga)
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 35J20 | Variational methods for second-order elliptic equations |
| 35J99 | Elliptic equations and elliptic systems |
| 35H99 | Close-to-elliptic equations |
| 52A40 | Inequalities and extremum problems involving convexity in convex geometry |
References:
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