Higher regularity for solutions to elliptic systems in divergence form subject to mixed boundary conditions

DOI10.1007/s10231-018-0818-9zbMath1420.35056OpenAlexW2906426070WikidataQ128695971 ScholiaQ128695971MaRDI QIDQ2315229

Hannes Meinlschmidt, Winnifried Wollner, Robert Haller-Dintelmann

Publication date: 1 August 2019

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-018-0818-9

zbMATH Keywords

interpolation theorynon-Lipschitz coefficientsquadratic gradient termsBessel potential scalemaximal elliptic regularityphase-field damagesecond-order divergence operators

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Quasilinear elliptic equations (35J62) Boundary value problems for second-order elliptic systems (35J57)

Related Items (8)

Optimizing Fracture Propagation Using a Phase-Field Approach ⋮ A priorierror estimates for the space-time finite element approximation of a quasilinear gradient enhanced damage model ⋮ Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations ⋮ Second-order optimality conditions for an optimal control problem governed by a regularized phase-field fracture propagation model ⋮ A Stochastic Gradient Method With Mesh Refinement for PDE-Constrained Optimization Under Uncertainty ⋮ An Optimal Control Problem Governed by a Regularized Phase-Field Fracture Propagation Model. Part II: The Regularization Limit ⋮ A priori error estimates for a linearized fracture control problem ⋮ A Posteriori Estimator for the Adaptive Solution of a Quasi-Static Fracture Phase-Field Model with Irreversibility Constraints

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