Error analysis of a diffuse interface method for elliptic problems with Dirichlet boundary conditions

AbstractWe study existence and regularity of the solutions for some anisotropic elliptic problems with homogeneous Dirichlet boundary conditions in bounded domains.

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On weak Dirichlet boundary conditions for elliptic problems in the continuous Galerkin method

Journal of Computational Physics ◽

10.1016/j.jcp.2019.05.021 ◽

2019 ◽

Vol 394 ◽

pp. 732-744

Author(s):

Martin Vymazal ◽

David Moxey ◽

Chris D. Cantwell ◽

Spencer J. Sherwin ◽

Robert M. Kirby

Keyword(s):

Boundary Conditions ◽

Galerkin Method ◽

Dirichlet Boundary ◽

Elliptic Problems ◽

Dirichlet Boundary Conditions ◽

Continuous Galerkin

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Multiplicity Results for a Class of Asymptotically Linear Elliptic Problems With Resonance and Applications to Problems With Measure Data

Advanced Nonlinear Studies ◽

10.1515/ans-2010-0210 ◽

2010 ◽

Vol 10 (2) ◽

Cited By ~ 1

Author(s):

Alberto Ferrero ◽

Claudio Saccon

Keyword(s):

Boundary Conditions ◽

Bounded Domain ◽

Dirichlet Boundary ◽

Elliptic Problems ◽

Dirichlet Boundary Conditions ◽

Measure Data ◽

Dirichlet Problems ◽

Asymptotically Linear ◽

Multiplicity Results ◽

Existence And Multiplicity

AbstractWe study existence and multiplicity results for solutions of elliptic problems of the type -Δu = g(x; u) in a bounded domain Ω with Dirichlet boundary conditions. The function g(x; s) is asymptotically linear as |s| → +∞. Also resonant situations are allowed. We also prove some perturbation results for Dirichlet problems of the type -Δu = g

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Overlapping domain decomposition for elliptic problems on locally refined meshes: Dirichlet boundary conditions

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2002-0602 ◽

2002 ◽

Vol 17 (6) ◽

Author(s):

V. V. Akimov

Keyword(s):

Boundary Conditions ◽

Domain Decomposition ◽

Dirichlet Boundary ◽

Elliptic Problems ◽

Dirichlet Boundary Conditions ◽

Refined Meshes ◽

Overlapping Domain Decomposition ◽

Locally Refined Meshes

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

Journal of High Energy Physics ◽

10.1007/jhep01(2021)039 ◽

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.

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Charge algebra in Al(A)dSn spacetimes

Journal of High Energy Physics ◽

10.1007/jhep05(2021)210 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Adrien Fiorucci ◽

Romain Ruzziconi

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Three Dimensional ◽

Dirichlet Boundary Conditions ◽

Boundary Structure ◽

Asymptotic Symmetry ◽

Renormalization Procedure ◽

Field Dependent ◽

Odd Dimensions

Abstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

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