On the modulus of continuity of the solution to the Dirichlet problem at a regular boundary point

1972 ◽  
Vol 12 (1) ◽  
pp. 472-475
Author(s):  
A. A. Novruzov
Keyword(s):  
Dirichlet Problem ◽  
Modulus Of Continuity ◽  
Boundary Point ◽  
Regular Boundary

scholarly journals A Boundary Estimate for Singular Sub-Critical Parabolic Equations

2020 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Boundary Point ◽  
Cylindrical Domain ◽  
Boundary Estimate ◽  
Critical Range ◽  
Type Integral ◽  
Wiener Type ◽  
Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

scholarly journals A Remark on the Continuous Subsolution Problem for the Complex Monge-Ampère Equation

2019 ◽  
Vol 45 (1) ◽  
pp. 83-91
Author(s):  
Sławomir Kołodziej ◽  
Ngoc Cuong Nguyen
Keyword(s):  
Dirichlet Problem ◽  
Modulus Of Continuity ◽  
Continuous Solution ◽  
Type Condition ◽  
Right Hand ◽  
The Right ◽  
Monge Ampere

Abstract We prove that if the modulus of continuity of a plurisubharmonic subsolution satisfies a Dini-type condition then the Dirichlet problem for the complex Monge-Ampère equation has the continuous solution. The modulus of continuity of the solution also given if the right hand side is locally dominated by capacity.

Behavior of solutions of the Dirichlet Problem for the $p(x)$-Laplacian at a boundary point

2020 ◽  
Vol 31 (2) ◽  
pp. 251-271 ◽  
Author(s):  
Yu. A. Alkhutov ◽  
M. D. Surnachev
Keyword(s):  
Dirichlet Problem ◽  
Boundary Point
Sign in / Sign up

Export Citation Format

Share Document