Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
Donatella Danielli, Nicola Garofalo, Arshak Petrosyan, Tung To
TL;DR
This paper provides a comprehensive analysis of the parabolic Signorini problem, establishing optimal regularity of solutions, classifying free boundary points, and describing the structure of both regular and singular sets.
Contribution
It introduces a generalized Almgren's monotonicity formula to prove optimal regularity and classify free boundary points in the parabolic Signorini problem.
Findings
Proved optimal regularity of solutions.
Classified free boundary points into regular and singular types.
Described the structure of the regular and singular sets.
Abstract
We give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's monotonicity of the frequency. This includes the proof of the optimal regularity of solutions, classification of free boundary points, the regularity of the regular set and the structure of the singular set.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Numerical methods in inverse problems · Advanced Mathematical Modeling in Engineering