scholarly journals On a class of non-elliptic boundary problems

1974 ◽  
Vol 54 ◽  
pp. 7-20 ◽  
Author(s):  
Yoshio Kato
Keyword(s):  
Differential Equation ◽  
Bounded Domain ◽  
Elliptic Boundary ◽  
Second Order ◽  
Elliptic Differential Equation ◽  
Boundary Problems

Let Ω be a bounded domain in Rl (l ≥ 2) with, C∞ boundary Γ of dimension l — 1 and let there be given a second order elliptic differential equation(1) in Ω,where ∂j = ∂/∂xi and all coefficients are assumed, for the sake of simplicity, to be real-valued and C∞ on .

scholarly journals On non-elliptic boundary problems

1982 ◽  
Vol 86 ◽  
pp. 1-38
Author(s):  
Yoshio Kato
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Elliptic Differential Equation ◽  
Boundary Problems

The purpose of this paper is to study the boundary value problems for the second order elliptic differential equation

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

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.

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