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search.filters.applied.f.access: openAccess × End date: 2019 × Start date: 2018 × End date: 2009 × Start date: 2000 × Type: Text × Subject: regularity × Subject: uniqueness × WGL Institute: WIAS ×

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    Resolvent estimates in W-1,p related to strongly coupled linear parabolic systems with coupled nonsmooth capacities
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Glitzky, Annegret; Hünlich, Rolf
    We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W-1,p spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain Lp estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result.
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    Regularity and uniqueness in quasilinear parabolic systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Krejčí, Pavel; Panizzi, Lucia
    Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.