Dirichlet problem for holomorphic functions in generalized Hölder spaces

2010 ◽  
Vol 81 (3) ◽  
pp. 403-405
Author(s):  
V. V. Napalkov ◽  
A. Yu. Timofeev
Keyword(s):  
Dirichlet Problem ◽  
Holomorphic Functions ◽  
Hölder Spaces ◽  
Holder Spaces

scholarly journals The equation divu + 〈a,u〉 = f

2019 ◽  
Vol 22 (04) ◽  
pp. 1950035
Author(s):  
Pierre Bousquet ◽  
Gyula Csató
Keyword(s):  
Dirichlet Problem ◽  
Vector Field ◽  
Existence Results ◽  
Hölder Spaces ◽  
Existence Of A Solution ◽  
Divergence Operator ◽  
Necessary And Sufficient ◽  
First Time ◽  
Holder Spaces

We study the solutions [Formula: see text] to the equation [Formula: see text] where [Formula: see text] and [Formula: see text] are given. We significantly improve the existence results of [G. Csató and B. Dacorogna, A Dirichlet problem involving the divergence operator, Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016) 829–848], where this equation has been considered for the first time. In particular, we prove the existence of a solution under essentially sharp regularity assumptions on the coefficients. The condition that we require on the vector field [Formula: see text] is necessary and sufficient. Finally, our results cover the whole scales of Sobolev and Hölder spaces.

MIXED FRACTIONAL DIFFERENTIATION OPERATORS IN HÖLDER SPACES DEFINED BY USUAL HÖLDER CONDITION

2019 ◽  
Author(s):  
T. Mamatov ◽  
R. Sabirova ◽  
D. Barakaev
Keyword(s):  
Fractional Derivative ◽  
Fractional Differentiation ◽  
Hölder Condition ◽  
Hölder Spaces ◽  
Main Interest ◽  
Hölder Class ◽  
Holder Class ◽  
Function Of Two Variables ◽  
Holder Spaces

We study mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The main interest being in the evaluation of the latter for the mixed fractional derivative in the cases Hölder class defined by usual Hölder condition

Solvability in Hölder spaces of an integral equation which models dynamics of the capillary rise

2020 ◽  
Vol 490 (1) ◽  
pp. 124237
Author(s):  
Hanna Okrasińska-Płociniczak ◽  
Łukasz Płociniczak ◽  
Juan Rocha ◽  
Kishin Sadarangani
Keyword(s):  
Integral Equation ◽  
Capillary Rise ◽  
Hölder Spaces ◽  
Holder Spaces
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