Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations
DOI10.1016/j.jde.2021.01.032zbMath1464.35088arXiv2003.11379OpenAlexW3126834790MaRDI QIDQ2656285
Hannes Meinlschmidt, Joachim Rehberg
Publication date: 11 March 2021
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.11379
fractional Sobolev spaceselliptic regularitysemiconductor equationsnonsmooth geometryvan Roosbroeck systemSneiberg stability theorem
Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Classical flows, reactions, etc. in chemistry (92E20) PDEs with low regular coefficients and/or low regular data (35R05) PDEs in connection with semiconductor devices (35Q81)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hölder-estimates for non-autonomous parabolic problems with rough data
- A note on function spaces in rough domains
- Maximal parabolic regularity for divergence operators including mixed boundary conditions
- Classical solutions of drift-diffusion equations for semiconductor devices: The two-dimensional case
- Semigroups of linear operators and applications to partial differential equations
- A \(W^{1,p}\)-estimate for solutions to mixed boundary value problems for second order elliptic differential equations
- Complete blow-up after \(T_{\max}\) for the solution of a semilinear heat equation
- An \(H^S\)-regularity result for the gradient of solutions to elliptic equations with mixed boundary conditions
- Geometric theory of semilinear parabolic equations
- Regularity results for elliptic equations in Lipschitz domains
- The Cauchy problem for \(u_{t}=\Delta u+| \nabla u|^q\)
- Nonlocal self-improving properties: a functional analytic approach
- Maximal regularity for evolution equations in weighted \(L_p\)-spaces
- Asymptotic properties of solutions of the viscous Hamilton-Jacobi equation
- Nonregular pseudo-differential operators
- \(L^p\)-estimates for the square root of elliptic systems with mixed boundary conditions
- 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
- Weak solutions to Fokker-Planck equations and mean field games
- Higher regularity for solutions to elliptic systems in divergence form subject to mixed boundary conditions
- Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets
- The square root problem for second-order, divergence form operators with mixed boundary conditions on \(L^p\)
- Elliptic model problems including mixed boundary conditions and material heterogeneities
- Optimal regularity for elliptic transmission problems including \(C^1\) interfaces
- The functional calculus for sectorial operators
- Regularization of mixed second-order elliptic problems
- Elliptic and parabolic regularity for second- order divergence operators with mixed boundary conditions
- Theory of Sobolev Multipliers
- On traces of Sobolev functions on the boundary of extension domains
- ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
- The full Keller–Segel model is well-posed on nonsmooth domains
- The 3D transient semiconductor equations with gradient-dependent and interfacial recombination
- Optimal Sobolev Regularity for Linear Second-Order Divergence Elliptic Operators Occurring in Real-World Problems
- 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
- Superlinear Parabolic Problems
- Analytic semigroups and optimal regularity in parabolic problems
- Solvability and maximal regularity of parabolic evolution equations with coefficients continuous in time
This page was built for publication: Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations
