Axiomatic theory of Sobolev spaces
Expositiones Mathematicae, 2001 Let \((X,d,\mu)\) be a set \(X\), equipped with a metric \(d\) and a Borel measure \(\mu\). For any \(u\in L^{\text{loc}}_p (X)\), so-called pseudo-gradients \(D[u]\) are introduced axiomatically, and on this basis \(p\)-Dirichlet energies, which, in turn, are used to introduce Sobolev spaces \(W^1_p (X)\).
Marc Troyanov, Vladimir Gol'dshtein
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Traces of multipliers in pairs of weighted Sobolev spaces
Journal of Function Spaces and Applications, 2005 We prove that the pointwise multipliers acting in a pair of fractional Sobolev spaces form the space of boundary traces of multipliers in a pair of weighted Sobolev space of functions in a domain.
Vladimir Maz'ya, Tatyana Shaposhnikova
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New characterizations of magnetic Sobolev spaces
Advances in Nonlinear Analysis, 2018 We establish two new characterizations of magnetic Sobolev spaces for Lipschitz magnetic fields in terms of nonlocal functionals. The first one is related to the BBM formula, due to Bourgain, Brezis and Mironescu. The second one is related to the work of
Nguyen Hoai-Minh +3 more
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The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities. [PDF]
Calc Var Partial Differ Equ, 2023 Sodini GE.
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Weighted Sobolev Spaces on Metric Measure Spaces
, 2015 We investigate weighted Sobolev spaces on metric measure spaces $(X,d,m)$. Denoting by $\rho$ the weight function, we compare the space $W^{1,p}(X,d,\rho m)$ (which always concides with the closure $H^{1,p}(X,d,\rho m)$ of Lipschitz functions) with the ...
Ambrosio, Luigi +2 more
core
A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I. [PDF]
Rev Mat Complut, 2023 Comi GE, Stefani G.
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On the identity of Morrey-Calkin and Schauder-Sobolev spaces [PDF]
, 1956 P. Szeptycki
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The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces. [PDF]
Calc Var Partial Differ Equ, 2021 Guerra A, Koch L, Lindberg S.
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Approximation Theory of Multivariate Spline Functions in Sobolev Spaces [PDF]
, 1969 Martin H. Schultz
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Quasi‐invariance of Gaussian measures for the 3d$3d$ energy critical nonlinear Schrödinger equation
Communications on Pure and Applied Mathematics, Volume 78, Issue 12, Page 2305-2353, December 2025.Abstract We consider the 3d$3d$ energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator (1−Δ)−s$(1-\Delta)^{-s}$, where Δ$\Delta$ is the Laplace operator and s$s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple
Chenmin Sun, Nikolay Tzvetkov
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