Superposition operators in Sobolev spaces

By S. Vodop’yanov, A. Ukhlov. 2002

107 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/364c41631affc2c47c9b9d16080cd5195ed9cc42

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1. A. Ukhlov
2. V. Gol’dshtein

Citations in the corpus

• The spectral estimates for the Neumann-Laplace operator in space domains (2016, background): “ such points. Then [10] |J(x,ϕ)||∇f|(ϕ(x)) ≤|∇(f ◦ϕ)|(x)adjDϕ(x) for almost all x ∈Ω. THE SPECTRAL NEUMANN PROBLEM FOR THE LAPLACE OPERATOR 19 Because pre-image of a set measure zero has measure zero [29], we obtain kf |L1 ∞(Ω)ek= esssup y∈Ωe |∇f|(y) = esssup x∈Ω |∇f|(ϕ(x)) ≤esssup x∈Ω |∇(f ◦ϕ)|(ϕ(x”