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On the Critical Point Regularity for Degenerate Diffusive Equations

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Abstract

We investigate regularity estimates at interior critical points of solutions to p-degenerate elliptic equations in a heterogeneous medium. If the source term is away from zero, we obtain a quantitative non-degeneracy estimate, which implies that solutions can never be smoother than \(C^{p\prime }\) at critical points. At zero source critical points, however, we establish higher order regularity estimates, which are sharp with respect to the source vanishing rate.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, FL, USA

    Eduardo V. Teixeira

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  1. Eduardo V. Teixeira
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Correspondence to Eduardo V. Teixeira.

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Communicated by G. Dal Maso.

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Teixeira, E.V. On the Critical Point Regularity for Degenerate Diffusive Equations. Arch Rational Mech Anal 244, 293–316 (2022). https://doi.org/10.1007/s00205-022-01768-2

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