For a general open set, we characterize the compactness of the embedding for the homogeneous Sobolev space D1,p → Lq in 0 terms of the summability of its torsion function. In particular, for 1 ≤ q < p we obtain that the embedding is continuous if and only if it is compact. The proofs crucially exploit a torsional Hardy inequality that we investigate in detail.
Compact Sobolev embeddings and torsion functions / Brasco L; Ruffini B. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 34:4(2017), pp. 817-843. [10.1016/j.anihpc.2016.05.005]
Compact Sobolev embeddings and torsion functions
Ruffini B
2017
Abstract
For a general open set, we characterize the compactness of the embedding for the homogeneous Sobolev space D1,p → Lq in 0 terms of the summability of its torsion function. In particular, for 1 ≤ q < p we obtain that the embedding is continuous if and only if it is compact. The proofs crucially exploit a torsional Hardy inequality that we investigate in detail.File in questo prodotto:
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