Pointwise Differentiability and Absolute Continuity
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Publication:4047781
DOI10.2307/1996986zbMath0295.26013OpenAlexW4242294712MaRDI QIDQ4047781
William P. Ziemer, Thomas Bagby
Publication date: 1974
Full work available at URL: https://doi.org/10.2307/1996986
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuity and differentiation questions (26B05)
Related Items (34)
Functions from Sobolev and Besov spaces with maximal Hausdorff dimension of the exceptional Lebesgue set ⋮ A capacitary weak type inequality for Sobolev functions and its applications ⋮ Differentiability properties of Orlicz-Sobolev functions ⋮ On a generalization of \(L^p\)-differentiability ⋮ Pointwise behaviour of \(M^{1,1}\) Sobolev functions ⋮ On the rate of convergence of the finite-difference approximations for parabolic Bellman equations with constant coefficients ⋮ The Gauss--Green theorem and removable sets for PDEs in divergence form ⋮ Lusin-type properties of convex functions and convex bodies ⋮ Taylor's inequalities in Orlicz–Sobolev type spaces ⋮ Behavior at the boundary of solutions of quasilinear parabolic equations ⋮ Hölder continuity of the traces of Sobolev functions to hypersurfaces in Carnot groups and the \(\mathcal{P} \)-differentiability of Sobolev mappings ⋮ Differentiation of Besov spaces and the Nikodym maximal operator ⋮ Topological properties of mappings with finite distortion on Carnot groups ⋮ Gauss's theorem and the self-adjointness of Schrödinger operators ⋮ Hausdorff dimension of Lebesgue sets for \(W \alpha p\) classes on metric spaces ⋮ Thermal capacity and boundary regularity ⋮ A pointwise convergence for Sobolev space functions. ⋮ Subdifferentiable functions satisfy Lusin properties of class \(C^1\) or \(C^2\) ⋮ Fine properties of functions from Hajłasz-Sobolev classes \(M_\alpha^p\), \(p > 0\). I: Lebesgue points ⋮ Differentiability properties of Bessel potentials and Besov functions ⋮ \(L^p\)-Taylor approximations characterize the Sobolev space \(W^{1,p}\) ⋮ A remark on Calderón-Zygmund classes and Sobolev spaces ⋮ On the instability of capacity ⋮ An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces ⋮ Colloquium lectures on geometric measure theory ⋮ Two approximation problems in function spaces ⋮ The Luzin approximation of functions from classes \(W_\alpha ^p\) on metric spaces with measure ⋮ On the Differentiability of Lipschitz-Besov Functions ⋮ Weighted Capacity and the Choquet Integral ⋮ On Functions with Summable Approximate Peano Derivative ⋮ Differentiability of logarithmic Besov functions in terms of capacities ⋮ Singular sets of Sobolev functions ⋮ Strong Differentiability Properties of Bessel Potentials ⋮ Extensions of Meyers-Ziemer results
Cites Work
- Functional spaces and functional completion
- The divergence theorem for discontinuous vector fields
- On a conjecture of J. Serrin
- Polar sets and removable singularities of partial differential equations
- Green-Goursat theorem
- Smoothness and differentiability in $L_{p}$
- On Functions with Summable Derivative
- A Theory of Capacities for Potentials of Functions in Lebesgue Classes.
- The Equivalence of Two Definitions of Capacity
- On a theorem of F. Riesz
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