$L^P$-uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients

Vitali Liskevich; Michael Röckner; Zeev Sobol; Oleksiy Us

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Anna Canale, Patrizia Di Gironimo, Antonio Vitolo (1998)

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We introduce a sort of "local" Morrey spaces and show an existence and uniqueness theorem for the Dirichlet problem in unbounded domains for linear second order elliptic partial differential equations with principal coefficients "close" to functions having derivatives in such spaces.

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We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yoshida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.

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Displaying similar documents to “ L P -uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients”

Displaying similar documents to “ $L^{P}$ -uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients”