Boundary-value problems for linear elliptic and parabolic equations with discontinuous coefficients

1964 ◽  
pp. 175-194 ◽  
Author(s):  
O. A. Oleĭnik
Keyword(s):  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Discontinuous Coefficients ◽  
Elliptic And Parabolic Equations

On corner singularities of solutions to mixed boundary-value problems for second-order elliptic and parabolic equations

1991 ◽  
Vol 433 (1887) ◽  
pp. 209-217 ◽  
Keyword(s):  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Corner Singularities ◽  
Mixed Boundary Value Problems ◽  
Decomposition Formula ◽  
Elliptic And Parabolic Equations ◽  
Time Dependent Problems

In this paper we prove a decomposition formula for solutions of mixed boundary-value problems for elliptic and parabolic equations into regular and singular parts, which provides an explicit description of the behaviour of the solution near the corners of the boundary and also, in parabolic cases, shows how the singularity due to the corners varies in time. We also give some sufficient conditions for the regularity of the solution of time-dependent problems.

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