On Cauchy-Dirichlet Problem in Half-Space for Linear Integro-Differential Equations in Weighted Hoelder Spaces

Remigijus Mikulevicius (University of Southern California)
Henrikas Pragarauskas (Institute of Mathematics and Informatics)

Abstract


We study the Cauchy-Dirichlet problem in half-space for linear parabolic integro-differential equations. Sufficient conditions are derived under which the problem has a unique solution in weighted Hoelder classes. The result can be used in the regularity analysis of certain functionals arising in the theory of Markov processes.

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Pages: 1398-1416

Publication Date: December 16, 2005

DOI: 10.1214/EJP.v10-292

References

  1. J. M. Bony. Problem de Dirichlet et semi-groupe fortement fellerien associees a un operateur integrodifferentielle, C. R. Acad. Sci., 265 (1967), 362-364.
  2. M. G. Garroni and J.-L. Menaldi. Green Functions for Second Order Parabolic Integro-Differential Problems, Longman Scientific, Essex, 1992.
  3. D. Gilbarg and N. S. Trudinger. Elliptic Partial Differential Equations of Second Order, Springer, New York, 1983.
  4. G. Gimbert and P. L. Lions. Existence and regularity results for solutions of second order elliptic integrodifferential equations. Richerce di Matematica  33 (1984), 315-358.
  5. R. Mikulevicius and H. Pragarauskas. On classical solutions of boundary value problems for certain nonlinear integro-differential equations. Lithuanina Math. J. 34 (1994), 275-287.
  6. R. Mikulevicius and H. Pragarauskas. On Cauchy-Dirichlet problem in half-space for parabolic SPDEs in weighted Hoelder spaces. Stoch. Proc. Appl. 106 (2003), 185-222.
  7. L. Stupelis. Solvability of thye first boundary-value problem in W_{p,0}^{2}(Omega ) for a class of integro-differential equations. Lithuanian Math. J. 14 (1974), 502-506.
  8. L. Stupelis. Navier-Stokes Equations in Irregular Domains. Kluwer, Dordrecht, 1995.
     
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