Thin obstacle problem: estimates of the distance to the exact solution

DOI10.4171/IFB/410zbMath1407.35231arXiv1703.06357OpenAlexW2614933081WikidataQ109299496 ScholiaQ109299496MaRDI QIDQ1729841

Darya E. Apushkinskaya, Sergey I. Repin

Publication date: 28 February 2019

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.06357

zbMATH Keywords

free boundary problemsthin obstacleestimates of the distance to the exact solutionvariationals problems

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Free boundary problems for PDEs (35R35) Variational methods for second-order elliptic equations (35J20)

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Functional a posteriori error estimates for the parabolic obstacle problem ⋮ Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions

Cites Work

• Explicit constants in Poincaré-type inequalities for simplicial domains and application to a posteriori estimates
• Boundary Harnack estimates in slit domains and applications to thin free boundary problems
• Higher regularity of the free boundary in the elliptic Signorini problem
• An optimal Poincaré inequality for convex domains
• Optimal regularity for the Signorini problem
• Two dimensional variational problems with thin obstacles
• Estimates of deviations from exact solutions of elliptic variational inequalities
• Global solutions of an obstacle-problem-like equation with two phases
• Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• The two-phase membrane problem--an intersection-comparison approach to the regularity at branch points
• A posteriori error estimates for two-phase obstacle problem
• On the coincidence set in variational inequalities
• Optimal regularity of lower dimensional obstacle problems
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Exact constants in Poincaré type inequalities for functions with zero mean boundary traces
• The structure of the free boundary for lower dimensional obstacle problems
• Further regularity for the signorini problem
• Financial Modelling with Jump Processes
• A posteriori error estimation for variational problems with uniformly convex functionals
• The Two-Phase Membrane Problem--Regularity of the Free Boundaries in Higher Dimensions
• Variational inequalities
• Approximations in elasticity based on the concept of function space
• An obstacle-problem-like equation with two phases: Pointwise regularity of the solution and an estimate of the Hausdorff dimension of the free boundary
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