Hölder regularity for a class of doubly non linear PDEs

2025/10/23 by Cassanello, Filippo Maria, Henriques, Eurica
#35B65 #35K55 #35K65 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.20432

Abstract

We prove local Hölder continuity for non negative, locally bounded, local weak solutions to the class of doubly nonlinear parabolic equations ∂_t (u_q) - div (|Du|^p-2 Du) = 0 for p > 2, 0 < q < p-1. The proof relies on expansion of positivity results combined with the study of an alternative (related to DeGiorgi-type lemmas) and an exponential shift which allows us to deal with the intrinsic geometry associated to the problem.

Citations

• On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part III
• On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II
• On the Hölder regularity of signed solutions to a doubly nonlinear equation
• Local Hölder continuity for some doubly nonlinear parabolic equations in measure spaces

Related

• On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II
• On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part III
• Hölder regularity of weak solutions to nonlocal doubly degenerate parabolic equations
• Hölder regularity of doubly nonlinear nonlocal quasilinear parabolic equations in some mixed singular-degenerate regime
• Local Hölder continuity for some doubly nonlinear parabolic equations in measure spaces