scholarly journals Strictly elliptic operators with Dirichlet boundary conditions on spaces of continuous functions on manifolds

2019 ◽  
Vol 20 (3) ◽  
pp. 1005-1028 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Continuous Functions ◽  
Elliptic Operators ◽  
Dirichlet Boundary Conditions ◽  
Spaces Of Continuous Functions

scholarly journals Weak Convergence for a Class of Stochastic Fractional Equations Driven by Fractional Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Xichao Sun ◽  
Junfeng Liu
Keyword(s):  
Weak Convergence ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Dirichlet Boundary ◽  
Random Perturbation ◽  
Continuous Functions ◽  
Dirichlet Boundary Conditions ◽  
Fractional Noise ◽  
Fractional Heat Equation ◽  
Fractional Equations

We consider a class of stochastic fractional equations driven by fractional noise ont,x∈0,T×0,1  ∂u/∂t=Dδαu+ft,x,u+∂2BHt,x/∂t ∂x, with Dirichlet boundary conditions. We formally replace the random perturbation by a family of sequences based on Kac-Stroock processes in the plane, which approximate the fractional noise in some sense. Under some conditions, we show that the real-valued mild solution of the stochastic fractional heat equation perturbed by this family of noises converges in law, in the space𝒞0,T×0,1of continuous functions, to the solution of the stochastic fractional heat equation driven by fractional noise.

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 Charge algebra in Al(A)dSn spacetimes

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.

scholarly journals Fibonacci wavelet method for solving time-fractional telegraph equations with Dirichlet boundary conditions

2021 ◽  
pp. 104123
Author(s):  
Firdous A. Shah ◽  
Mohd Irfan ◽  
Kottakkaran S. Nisar ◽  
R.T. Matoog ◽  
Emad E. Mahmoud
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Wavelet Method ◽  
Telegraph Equations
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