scholarly journals The Laplacian on Cartesian products with mixed boundary conditions

2021 ◽  
Author(s):  
Albrecht Seelmann
Keyword(s):  
Sobolev Space ◽  
Boundary Conditions ◽  
Quadratic Forms ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Cartesian Products ◽  
Standard Definition ◽  
First Order ◽  
Tensor Representations ◽  
Definition Of

AbstractA definition of the Laplacian on Cartesian products with mixed boundary conditions using quadratic forms is proposed. Its consistency with the standard definition for homogeneous and certain mixed boundary conditions is proved and, as a consequence, tensor representations of the corresponding Sobolev spaces of first order are derived. Moreover, a criterion for the domain to belong to the Sobolev space of second order is proved.

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.

Differential Cubature Method for Static Solution of Laminated Shells of Revolution with Mixed Boundary Conditions

2011 ◽  
Vol 471-472 ◽  
pp. 1005-1009 ◽  
Author(s):  
S.M. Mousavi
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Shear Deformation Theory ◽  
Mixed Boundary Conditions ◽  
Static Solution ◽  
Computational Effort ◽  
Shells Of Revolution ◽  
Laminated Shells ◽  
First Order ◽  
Laminated Shells Of Revolution

The bending analysis of laminated shells of revolution, such as spherical, conical and cylindrical panels, is carried out utilizing the differential cubature method (DCM). To do so, a general software based on the DCM is developed which can tackle shells of revolution with symmetric and unsymmetric lamination sequence. Analysis of shells with general Loading and various combinations of clamped, simply supported, free and mixed boundary condition, may be carried out having acceptable accuracy. Using first order shear deformation theory, fifteen first order partial differential equations are obtained which contain fifteen unknowns in terms of displacements, rotations, moments and forces. Utilizing all of these equations results in the capability of the method to deal with any kinds of boundary conditions. Comparison of the results obtained by the DCM, shows very good agreement with the results of other numerical and analytical methods, while having less computational effort.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

scholarly journals Casimir effect for a massive scalar field under mixed boundary conditions

2003 ◽  
Vol 33 (4) ◽  
pp. 860-866 ◽  
Author(s):  
A.C. Aguiar Pinto ◽  
T.M. Britto ◽  
R. Bunchaft ◽  
F. Pascoal ◽  
F.S.S. da Rosa
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Casimir Effect ◽  
Mixed Boundary Conditions ◽  
Massive Scalar ◽  
Massive Scalar Field
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