scholarly journals Holder regularity of solutions of generalized p-Laplacian type parabolic equations

2012 ◽  
Author(s):  
Sukjung Hwang
Keyword(s):  
Parabolic Equations ◽  
Regularity Of Solutions ◽  
Hölder Regularity ◽  
Holder Regularity

scholarly journals Hölder regularity for degenerate parabolic equations with variable exponents

2022 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
Hamid EL Bahja
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Young’S Inequality ◽  
Scaling Method ◽  
Degenerate Parabolic ◽  
Young's Inequality ◽  
Holder Regularity

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 logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.

Regularity theory of Kolmogorov operator revisited

2020 ◽  
pp. 1-12
Author(s):  
Damir Kinzebulatov
Keyword(s):  
Elliptic Equation ◽  
Vector Fields ◽  
Regularity Theory ◽  
Regularity Of Solutions ◽  
Hölder Regularity ◽  
Kolmogorov Operator ◽  
Holder Regularity ◽  
Critical Order

Abstract We consider Kolmorogov operator $-\Delta +b \cdot \nabla $ with drift b in the class of form-bounded vector fields (containing vector fields having critical-order singularities). We characterize quantitative dependence of the Sobolev and Hölder regularity of solutions to the corresponding elliptic equation on the value of the form-bound of b.

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