On Weighted Sobolev Spaces

Chua, Seng-Kee

Canadian journal of mathematics, Tome 48 (1996) no. 3, pp. 527-541

Résumé

We study density and extension problems for weighted Sobolev spaces on bounded (ε, δ) domains D when a doubling weight w satisfies the weighted Poincaré inequality on cubes near the boundary of D and when it is in the Muckenhoupt A p class locally in D. Moreover, when the weights w i (x) are of the form dist(x, M i )αi , α i∈ R, M i ⊂ D that are doubling, we are able to obtain some extension theorems on (ε, ∞) domains.

Détail

DOI : 10.4153/CJM-1996-027-5

Mots-clés : 46E35, Poincaré inequalities, Ap weights, power weights, doubling, locally Ap weights, (ε, δ) and (ε, ∞) domains

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