Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets

DOI10.1007/s00041-019-09681-1zbMath1435.46016arXiv1807.02293OpenAlexW2963999088MaRDI QIDQ2326886

Moritz Egert, Sebastian Bechtel

Publication date: 10 October 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.02293

zbMATH Keywords

Hardy's inequalityinterpolation of Banach spacesporous sets(fractional) Sobolev spacesmeasure density conditionstraces and extensions of Sobolev functions

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Interpolation between normed linear spaces (46B70)

Related Items (11)

Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations ⋮ On the regularity of characteristic functions ⋮ Sparse optimal control of a quasilinear elliptic PDE in measure spaces ⋮ Dimension estimate for the two-sided points of planar Sobolev extension domains ⋮ \(L^p\)-estimates for the square root of elliptic systems with mixed boundary conditions. II ⋮ Kato square root problem for degenerate elliptic operators on bounded Lipschitz domains ⋮ The Kato square root problem on locally uniform domains ⋮ The square root of a parabolic operator ⋮ On the \(\mathrm{L}^p\)-theory for second-order elliptic operators in divergence form with complex coefficients ⋮ Higher regularity for solutions to elliptic systems in divergence form subject to mixed boundary conditions ⋮ Existence of global solutions for 2D fluid-elastic interaction with small data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on function spaces in rough domains
• Characterizations of Sobolev functions that vanish on a part of the boundary
• A discrete transform and decompositions of distribution spaces
• Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval
• Maximal parabolic regularity for divergence operators including mixed boundary conditions
• Well-posedness for coupled bulk-interface diffusion with mixed boundary conditions
• Weighted Hardy inequalities and the size of the boundary
• A \(W^{1,p}\)-estimate for solutions to mixed boundary value problems for second order elliptic differential equations
• Lectures on analysis on metric spaces
• Second order optimality conditions for optimal control of quasilinear parabolic equations
• Extending Sobolev functions with partially vanishing traces from locally \(({\epsilon},{\delta})\)-domains and applications to mixed boundary problems
• The Kato square root problem for mixed boundary conditions
• Hölder estimates for second-order operators on domains with rough boundary
• The square root problem for second-order, divergence form operators with mixed boundary conditions on \(L^p\)
• A unified framework for parabolic equations with mixed boundary conditions and diffusion on interfaces
• A note on the dimensions of Assouad and Aikawa
• Sobolev embeddings, extensions and measure density condition
• Elliptic and parabolic regularity for second- order divergence operators with mixed boundary conditions
• Notes on Wolff's Note on Interpolation Spaces
• Direct Methods in the Theory of Elliptic Equations
• ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
• Linear extension operators for restrictions of function spaces to irregular open sets
• Interpolation for Function Spaces Related to Mixed Boundary Value Problems
• Porous Sets and Quasisymmetric Maps
• The 3D transient semiconductor equations with gradient-dependent and interfacial recombination
• Optimal Control of the Thermistor Problem in Three Spatial Dimensions, Part 2: Optimality Conditions
• Optimal Control of the Thermistor Problem in Three Spatial Dimensions, Part 1: Existence of Optimal Solutions
• Local approximations and intrinsic characterization of spaces of smooth functions on regular subsets of ℝⁿ
• THE KATO SQUARE ROOT PROBLEM FOR MIXED BOUNDARY VALUE PROBLEMS
• A framework for fractional Hardy inequalities
• Fractional Sobolev extension and imbedding
• Équations différentielles abstraites
• Interpolation in $L^{p}$ with boundary conditions

This page was built for publication: Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets