Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order

1988 ◽  
Vol 19 (1) ◽  
pp. 172-203 ◽  
Author(s):  
I. Babuška ◽  
B. Q. Guo
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Elliptic Problems ◽  
Second Order ◽  
Linear Elliptic Equation

scholarly journals Fundamental solutions and surface distributions

1969 ◽  
Vol 16 (3) ◽  
pp. 255-257
Author(s):  
R. A. Adams ◽  
G. F. Roach
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problems ◽  
Bounded Domain ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Second Order ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Image Position

When studying the solutions of elliptic boundary value problems in a bounded, smoothly bounded domain D⊂Rn we often encounter the formulawhere u(x)∈C2(D)∩C′(D̄) is a solution of the second order self-adjoint elliptic equationand denotes differentiation along the inward normal to ∂D at x∈∂D.

Modified Boundary Value Problems For a Quasi-Linear Elliptic Equation

1956 ◽  
Vol 8 ◽  
pp. 203-219 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Continuous Function ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Linear Elliptic Equation ◽  
Partial Differential

1. Introduction. The quasi-linear elliptic partial differential equation to be studied here has the form(1.1) Δu = − F(P,u).Here Δ is the Laplacian while F(P,u) is a continuous function of a point P and the dependent variable u. We shall study the Dirichlet problem for (1.1) and will find that the usual formulation must be modified by the inclusion of a parameter in the data or the differential equation, together with a further numerical condition on the solution.

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