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search.filters.applied.f.access: openAccess × Author: Disser, Karoline × Author: Rehberg, Joachim × Start date: 2000 × DDC: 510 × Has files: Yes × Type: Text × Version: publishedVersion ×

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Now showing 1 - 5 of 5
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    Optimal Sobolev regularity for linear second-order divergence elliptic operators occurring in real-world problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Disser, Karoline; Kaiser, Hans-Christoph; Rehberg, Joachim
    On bounded three-dimensional domains, we consider divergence-type operators including mixed homogeneous Dirichlet and Neumann boundary conditions and discontinuous coefficient functions. We develop a geometric framework in which it is possible to prove that the operator provides an isomorphism of suitable function spaces. In particular, in these spaces, the gradient of solutions turns out to be integrable with exponent larger than the space dimension three. Relevant examples from real-world applications are provided in great detail.
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    The 3D transient semiconductor equations with gradient-dependent and interfacial recombination
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Disser, Karoline; Rehberg, Joachim
    We establish the well-posedness of the transient van Roosbroeck system in three space dimensions under realistic assumptions on the data: non-smooth domains, discontinuous coefficient functions and mixed boundary conditions. Moreover, within this analysis, recombination terms may be concentrated on surfaces and interfaces and may not only depend on chargecarrier densities, but also on the electric field and currents. In particular, this includes Avalanche recombination. The proofs are based on recent abstract results on maximal parabolic and optimal elliptic regularity of divergence-form operators.
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    Hölder estimates for parabolic operators on domains with rough boundary
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Disser, Karoline; Rehberg, Joachim; Elst, A.F.M. ter
    In this paper we investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain including a very weak compatibility condition between the Dirichlet boundary part and its complement we prove Hölder continuity of the solution in space and time.
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    On maximal parabolic regularity for non-autonomous parabolic operators
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Disser, Karoline; Elst, A.F.M. ter; Rehberg, Joachim
    We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r ≠ 2. This allows us to prove maximal parabolic Lr-regularity for discontinuous non-autonomous second-order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations.
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    A unified framework for parabolic equations with mixed boundary conditions and diffusion on interfaces
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Disser, Karoline; Meyries, Martin; Rehberg, Joachim
    In this paper we consider scalar parabolic equations in a general non-smooth setting with emphasis on mixed interface and boundary conditions. In particular, we allow for dynamics and diffusion on a Lipschitz interface and on the boundary, where diffusion coefficients are only assumed to be bounded, measurable and positive semidefinite. In the bulk, we additionally take into account diffusion coefficients which may degenerate towards a Lipschitz surface. For this problem class, we introduce a unified functional analytic framework based on sesquilinear forms and show maximal regularity for the corresponding abstract Cauchy problem.