On Hölder continuity of solutions and their derivatives of linear and quasilinear elliptic and parabolic equations

1967 ◽  
pp. 207-269 ◽  
Author(s):  
O. A. Ladyženskaja ◽  
N. N. Ural′ceva
Keyword(s):  
Parabolic Equations ◽  
Hölder Continuity ◽  
Holder Continuity ◽  
Continuity Of Solutions ◽  
Elliptic And Parabolic Equations ◽  
Quasilinear Elliptic ◽  
Derivatives Of

\mathfrak{B}_{1} classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth

2019 ◽  
Vol 16 (3) ◽  
pp. 403-447
Author(s):  
Igor Skrypnik ◽  
Mykhailo Voitovych
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Hölder Continuity ◽  
Growth Conditions ◽  
Holder Continuity ◽  
Nonstandard Growth ◽  
Elliptic And Parabolic Equations ◽  
Functional Classes ◽  
Nonstandard Growth Conditions ◽  
Quasilinear Elliptic

The article provides an application of the generalized De Giorgi functional classes to the proof of the Hölder continuity of weak solutions to quasilinear elliptic and parabolic equations with nonstandard growth conditions.

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