B₁ classes of DeGiorgi-Ladyzhenskaya-Ural'tseva and their applications to elliptic and parabolic equations with generalized Orlicz growth conditions

2020/06/10 by Igor I. Skrypnik, Skrypnik, Igor I., Mykhailo V. Voitovych +1
Mathematics · #35D30 #35J62 #35K59 #49N60 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2006.05764

openalex publication_date 2020/06/10 · openalex created_date 2020/06/19 · openalex updated_date 2026/07/28

Abstract

We introduce elliptic and parabolic B₁ classes that generalize the well-known \mathfrakB_p classes of DeGiorgi, Ladyzhenskaya and Ural'tseva with p>1. New classes are applied to prove pointwise continuity of solutions of elliptic and parabolic equations with nonstandard growth conditions. Our considerations cover new cases of variable exponent and (p, q)-phase growth including the ,,singular-degenerate'' parabolic case p<2

Related

• On the continuity of solutions of quasilinear parabolic equations with\n generalized Orlicz growth under non-logarithmic conditions
• Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions
• Higher integrability for parabolic PDEs with generalized Orlicz growth
• Gradient regularity for strongly singular or degenerate elliptic and parabolic equations
• Gradient estimates for parabolic problems with Orlicz growth and discontinuous coefficients