HÖLDER REGULARITY OF SOLUTIONS OF PDE'S: A GEOMETRICAL VIEW

2001 ◽  
Vol 26 (7-8) ◽  
pp. 1145-1173 ◽  
Author(s):  
H. Aimar ◽  
L. Forzani ◽  
R. Toledano
Keyword(s):  
Regularity Of Solutions ◽  
Hölder Regularity ◽  
Holder Regularity

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.

scholarly journals New interpolation spaces and strict Hölder regularity for fractional abstract Cauchy problem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Md Mansur Alam ◽  
Shruti Dubey ◽  
Dumitru Baleanu
Keyword(s):  
Cauchy Problem ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Analytic Semigroup ◽  
Mild Solutions ◽  
Abstract Cauchy Problem ◽  
Regularity Of Solutions ◽  
Hölder Regularity ◽  
Interpolation Spaces ◽  
Holder Regularity

AbstractWe know that interpolation spaces in terms of analytic semigroup have a significant role into the study of strict Hölder regularity of solutions of classical abstract Cauchy problem (ACP). In this paper, we first construct interpolation spaces in terms of solution operators in fractional calculus and characterize these spaces. Then we establish strict Hölder regularity of mild solutions of fractional order ACP.

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