Carleson estimates for the singular parabolic -Laplacian in time-dependent domains

  • Ugo Gianazza

    Università di Pavia, Italy
Carleson estimates for the singular parabolic $p$-Laplacian in time-dependent domains cover

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Abstract

We deal with the parabolic -Laplacian in the so-called singular super-critical range , and we prove Carleson estimates for non-negative solutions in suitable non-cylindrical domains . The sets satisfy a proper NTA condition, tailored on the parabolic -Laplacian. As an intermediate step, we show that in these domains non-negative solutions which vanish at the boundary, are Hölder continuous up to the same boundary.

Cite this article

Ugo Gianazza, Carleson estimates for the singular parabolic -Laplacian in time-dependent domains. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 4, pp. 669–690

DOI 10.4171/RLM/953