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Hölder estimates for second-order operators with mixed boundary conditions
In this paper we investigate linear elliptic, second-order boundary value problems with mixed boundary conditions. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain
Hölder estimates for parabolic operators on domains with rough boundary
In this paper we investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain including a very weak compatibility condition between the Dirichlet boundary part and its complement we prove Hölder continuity of the solution in space and time.
Optimal Hölder index for density states of superprocesses with (1+[beta])-branching mechanism
For 0 < alpha leq 2, a super-alpha-stable motion X in R^d with branching of index 1 + beta in (1,2) is considered. If d < alpha / beta, a dichotomy for the density of states X_t at fixed times t > 0 holds: the density function is locally Hölder continuous if d = 1 and alpha > 1 + beta, but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal Hölder index.