Improved regularity estimates for degenerate or singular fully nonlinear dead-core systems and Hénon-type equations

2025/02/14 by Jiangwen Wang, Feida Jiang, Wang, Jiangwen +1 · 1 citation
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paper · pdf · doi:10.48550/arxiv.2502.10099

Abstract

In this paper, we study the degenerate or singular fully nonlinear dead-core systems coupled with strong absorption terms. We establish several properties, including improved regularity of viscosity solutions along the free boundary, non-degeneracy, a measure estimate of the free boundary, Liouville-type results, and the behavior of blow-up solution. We also derive sharp regularity estimates for viscosity solutions to Hénon-type equations with a degenerate weight and strong absorption, governed by a degenerate fully nonlinear operator. Our results are new even for the model equations involving degenerate Laplacian operators.

Citations

• The Alt–Phillips functional for negative powers
• Global regularity for a class of fully nonlinear PDEs with unbalanced variable degeneracy
• Fully nonlinear dead-core systems
• Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations
• Regularity properties for p−dead core problems and their asymptotic limit as p→∞
• Regularity for degenerate evolution equations with strong absorption
• Regularity for the fully nonlinear dead-core problem
• Infinity Laplacian equation with strong absorptions
• C 1 , α regularity of solutions of some degenerate fully non-linear elliptic equations
• Hausdorff Dimension and mean porosity
• The free boundary of a semilinear elliptic equation
• Schauder-type estimates for fully nonlinear degenerate elliptic equations

Cited by

• Regularity for fully nonlinear degenerate parabolic equations with strong absorption

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• Regularity for fully nonlinear degenerate parabolic equations with strong absorption
• Regularity for degenerate evolution equations with strong absorption
• Regularity for Fully Nonlinear P-Laplacian Parabolic Systems: the Degenerate Case