Holder Regularity for Degenerate Parabolic Equations with Variable Exponents

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By using the Steklov average and Young's inequality, we establish energy and logarithmic estimates for solutions to these equations. Then based on the intrinsic scaling method, we prove that local weak solutions are locally continuous.

Automated summary

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. Energy and logarithmic estimates for solutions to these equations are established using the Steklov average and Young's inequality. Furthermore, based on the intrinsic scaling method, it is proved that local weak solutions are locally continuous.