On Dirichlet's problem for quasi-linear elliptic equations

1974 ◽  
pp. 184-236 ◽  
Author(s):  
Robert P. Gilbert ◽  
George C. Hsiao
Keyword(s):  
Elliptic Equations ◽  
Dirichlet’S Problem

scholarly journals Smoothness Properties of Bounded Solutions of Dirichlet's Problem for Elliptic Equations in Regions with Corners on the Boundary

1980 ◽  
Vol 23 (2) ◽  
pp. 213-226 ◽  
Author(s):  
A. Azzam
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Smooth Boundary ◽  
Boundary Function ◽  
Bounded Solutions ◽  
Second Derivatives ◽  
Smoothness Of Solutions ◽  
Dirichlet’S Problem

We study here the smoothness of solutions of the Dirichlet problem for elliptic equations in a region G with a piece-wise smooth boundary. The smoothness of the solution given depends on the smoothness of the coefficients of the equation, the boundary, the boundary function and the values of the angles on the boundary and the values of the coefficients of the second derivatives at the corners.

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