Agradecimentos: This manuscript is part of the first author’s PhD thesis. E C Bezerra Júnior would like to thank the Department of Mathematics at Universidade Federal do Ceará for fostering a pleasant and productive scientific atmosphere, which has benefited a lot the final outcome of this project. E C Bezerra Júnior thanks to Capes-Brazil (Doctoral Scholarship). J V da Silva and G C Ricarte have been partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq-Brazil) under Grant Nos. 310303/2019-2 and304239/2021-6. J V da Silva has been partially supported by FAPDF Demanda Espontânea 2021 Ver menos

Abstract: In this manuscript, we establish C-loc(alpha,alpha/theta) regularity estimates for bounded weak solutions of a certain class of doubly degenerate evolution PDEs, whose simplest model case is given by partial derivative u/partial derivative t - div(m vertical bar u vertical bar(m-1)vertical bar del u vertical bar(p-2)del u) = f(x, t) in Omega(T): Omega x (0, T), where m >= 1, p >= 2 and f belongs to a suitable anisotropic Lebesgue space. Employing intrinsic scaling techniques and geometric tangential methods, we derive sharp regularity estimates for such models, which depend only on universal and compatibility parameters of the problem. In this scenario, our results are natural improvements for former ones in the context of nonlinear evolution PDEs with degenerate structure via a unified approach. As a consequence of our findings and approach, we address a Liouville type result for entire weak solutions of a related homogeneous problem with frozen coefficients and asymptotic estimates under a certain approximating regime, which may have their own mathematical interest. We also present examples of degenerate PDEs where our results can be applied Ver menos