scholarly journals Elliptic partial differential equations with mixed boundary conditions

1976 ◽  
Vol 15 (3) ◽  
pp. 475-476 ◽  
Author(s):  
A.J. Pryde
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential

PARTIAL DIFFERENTIAL EQUATIONS OF ELLIPTIC TYPE IN NONSMOOTH DOMAINS

2005 ◽  
Vol 07 (06) ◽  
pp. 787-808
Author(s):  
HELDER CANDIDO RODRIGUES
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Existence Result ◽  
Critical Case ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Elliptic Type ◽  
Nonsmooth Domains ◽  
Definition Of

This paper studies the problem -Δu + λu = up in nonsmooth domains with mixed boundary conditions. Special attention will be given here to the critical case and to domains which have no further regularity than a Lipschitzian boundary. For such domains, we obtain a generalized version of Cherrier's inequality and prove an existence result. This was achieved by using an extended definition of the manifold.

scholarly journals Spaces with homogeneous norms

1980 ◽  
Vol 21 (2) ◽  
pp. 189-205 ◽  
Author(s):  
A.J. Pryde
Keyword(s):  
Partial Differential Equations ◽  
Boundary Conditions ◽  
Sobolev Spaces ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Forthcoming Paper ◽  
Elliptic Partial Differential Equations ◽  
Riesz Potentials ◽  
Constant Coefficients ◽  
Homogeneous Norms

Spaces with homogeneous norms are closely related to the Beppo Levi spaces of Deny and Lions, to spaces of Riesz potentials, and to Sobolev spaces. In this paper we survey the literature on them, give a broad extension of their definition, and present their basic theory. Many of the properties of Sobolev spaces have their analogues. In fact, the two families are locally equivalent. Spaces with homogeneous norms are especially suited to the study of boundary value problems on for homogeneous elliptic operators with constant coefficients. We will use them extensively in a forthcoming paper to study elliptic partial differential equations with mixed boundary conditions on a smoothly bounded domain.

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