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Showing 1 to 3 of 3 for “"Holder continuity"”.
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Pointwise Schauder Estimates of Parabolic Equations in Carnot Groups
… Roughly speaking, the estimates state that the Holder continuity of the coefficient functions and inhomogeneous term implies the Holder continuity of the solution and its derivatives. This document establishes pointwise Schauder estimates for second order parabolic equations where the …
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Harnack inequality for nonlocal operators
Harnack inequalities are a fundamental property in both probability theory and analysis.The scale-variant Harnack inequalities play an important role in studying various properties, such as the regularity of harmonic functions in probability and analysis. This thesis focuses on scale-invariant …
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Some application of Malliavin calculus to SPDE and convergence of densities
… calculus is used to study the joint H"{o}lder continuity of the solution to a nonlinear SPDE arising from the study of one dimensional super-processes. Dawson, Vaillancourt and Wang [Ann. Inst. Henri. Poincaré Probab. Stat., 36 (2000) 167-180] proved that the solution of this SPDE gives the …