Results 121 to 130 of about 4,008,571 (171)
Resolvent estimates for elliptic systems in function spaces of higher regularity
Electronic Journal of Differential Equations, 2011 We consider parameter-elliptic boundary value problems and uniform a priori estimates in $L^p$-Sobolev spaces of Bessel potential and Besov type. The problems considered are systems of uniform order and mixed-order systems (Douglis-Nirenberg systems).
Robert Denk, Michael Dreher
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Existence of solutions to Burgers equations in domains that can be transformed into rectangles
Electronic Journal of Differential Equations, 2016 This work is concerned with Burgers equation $\partial _{t}u+u\partial_x u-\partial _x^2u=f$ (with Dirichlet boundary conditions) in the non rectangular domain $\Omega =\{(t,x)\in R^2 ...
Yassine Benia, Boubaker-Khaled Sadallah
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Embeddings of Anisotropic Sobolev Spaces
Archive for Rational Mechanics and Analysis, 1986This paper deals with the approximation and the entropy numbers of the embedding I of an anisotropic Sobolev space \(W^{r,p}(\Omega)\) into an Orlicz space \(L^{\phi}(\Omega)\), where \(\Omega\) is an open subset of \({\mathbb{R}}^ n\).
Edmunds, D. E., Edmunds, R. M.
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2018
AbstractThis chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded ...
D. E. Edmunds, W. D. Evans
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AbstractThis chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded ...
D. E. Edmunds, W. D. Evans
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Canadian Journal of Mathematics, 1996
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
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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
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Results in Mathematics, 2001
The paper contains the proof that certain \(L^2\)-Sobolev spaces on Riemannian manifolds with bounded curvature of all orders are equivalent. The main idea is to find suitable commutator estimates. Moreover the method is extended to Dirac-type operators.
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The paper contains the proof that certain \(L^2\)-Sobolev spaces on Riemannian manifolds with bounded curvature of all orders are equivalent. The main idea is to find suitable commutator estimates. Moreover the method is extended to Dirac-type operators.
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On one generalization of Sobolev spaces
Siberian Mathematical Journal, 1998In [Potential Anal. 5, No. 4, 403-415 (1996; Zbl 0859.46022)], \textit{P. Hajłasz} defined the Sobolev space \(S^1_p(X)\) on an arbitrary metric space.
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