On Cauchy-Dirichlet Problem for Linear Integro-Differential Equation in Weighted Sobolev Spaces

2007 ◽  
pp. 357-374 ◽  
Author(s):  
Remigijus Mikulevicius ◽  
Henrikas Pragarauskas
Keyword(s):  
Differential Equation ◽  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Integro Differential Equation

scholarly journals W2,p-Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Loredana Caso ◽  
Roberta D’Ambrosio ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Unique Solvability ◽  
Elliptic Equations ◽  
Weighted Sobolev Spaces ◽  
Elliptic Partial Differential Equations ◽  
Planar Case ◽  
Singular Data

We give an overview on some results concerning the unique solvability of the Dirichlet problem inW2,p,p>1, for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. We also extend such results to the planar case.

Existence of Solutions in Weighted Sobolev Spaces for Some Degenerate Quasilinear Elliptic Equations

2008 ◽  
Vol 15 (4) ◽  
pp. 627-634
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Quasilinear Elliptic Equations ◽  
Open Set ◽  
Quasilinear Elliptic

Abstract We prove an existence result for the Dirichlet problem associated to some degenerate quasilinear elliptic equations in a bounded open set Ω in in the setting of weighted Sobolev spaces .

The Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains of the plane

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Serena Boccia ◽  
Maria Salvato ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Uniqueness Result ◽  
Order Linear ◽  
A Priori Bound

AbstractThis paper deals with the Dirichlet problem for second order linear elliptic equations in unbounded domains of the plane in weighted Sobolev spaces. We prove an a priori bound and an existence and uniqueness result.

scholarly journals Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation

2021 ◽  
Author(s):  
G. Deligiannidis ◽  
S. Maurer ◽  
M. V. Tretyakov
Keyword(s):  
Differential Equation ◽  
Dirichlet Problem ◽  
Computational Cost ◽  
Activity Level ◽  
Currency Options ◽  
Euler Approximation ◽  
Integro Differential Equation ◽  
Time Stepping ◽  
Depth Analysis ◽  
Adaptive Time

AbstractWe consider stochastic differential equations driven by a general Lévy processes (SDEs) with infinite activity and the related, via the Feynman–Kac formula, Dirichlet problem for parabolic integro-differential equation (PIDE). We approximate the solution of PIDE using a numerical method for the SDEs. The method is based on three ingredients: (1) we approximate small jumps by a diffusion; (2) we use restricted jump-adaptive time-stepping; and (3) between the jumps we exploit a weak Euler approximation. We prove weak convergence of the considered algorithm and present an in-depth analysis of how its error and computational cost depend on the jump activity level. Results of some numerical experiments, including pricing of barrier basket currency options, are presented.

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