Browsing by Author "Elst, A.F.M. ter"
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- ItemConsistent operator semigroups and their interpolation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Elst, A.F.M. ter; Rehberg, JoachimUnder a mild regularity condition we prove that the generator of the interpolation of two C0-semigroups is the interpolation of the two generators.
- ItemHölder 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. terIn 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.
- ItemL ∞-estimates for divergence operators on bad domains(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Elst, A.F.M. ter; Rehberg, JoachimIn this paper, we prove L^infty-estimates for solutions of divergence operators in case of mixed boundary conditions. In this very general setting, the Dirichlet boundary part may be arbitrarily wild, i.e. no regularity conditions have to be imposed on it.
- ItemOn 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, JoachimWe 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.
- ItemParabolic equations with dynamical boundary conditions and source terms on interfaces(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Elst, A.F.M. ter; Meyries, Martin; Rehberg, JoachimWe consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative. Only minimal regularity assumptions on the domain and the coefficients are imposed. It is shown that the corresponding linear operator enjoys maximal parabolic regularity in a suitable Lp-setting. The linear results suffice to treat also the corresponding nondegenerate quasilinear problems.