On Weighted Sobolev Spaces
Copyright policy )On Weighted Sobolev Spaces
AbstractWe study density and extension problems for weighted Sobolev spaces on bounded (ε, δ) domains𝓓when a doubling weight w satisfies the weighted Poincaré inequality on cubes near the boundary of 𝓓 and when it is in the MuckenhouptApclass locally in 𝓓. Moreover, when the weightswi(x) are of the form dist(x,Mi)αi,αi∈ ℝ,Mi⊂ 𝓓that are doubling, we are able to obtain some extension theorems on (ε, ∞) domains.
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Power weights, power weights, Doubling, bounded \((\varepsilon,\delta)\) domains, (∈, Poincaré inequalities, weighted Sobolev spaces, Locally Ap weights, doubling, weighted Poincaré inequality, δ) and (∈, Muckenhoupt \(A_ p\) class, density and extension problems, ∞) domains, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Ap weights
Power weights, power weights, Doubling, bounded \((\varepsilon,\delta)\) domains, (∈, Poincaré inequalities, weighted Sobolev spaces, Locally Ap weights, doubling, weighted Poincaré inequality, δ) and (∈, Muckenhoupt \(A_ p\) class, density and extension problems, ∞) domains, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Ap weights
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