In this paper, we are interested in studying the Dirichlet problem for complex Monge-Ampère operator. We provide necessary and sufficient conditions to have Hölder continuous solutions.

The k-Hessian is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix. When k ≥ 2, the k-Hessian equation is a fully nonlinear partial differential equations. It is elliptic when restricted to k-admissible functions. In this paper we establish the existence and regularity of k-admissible solutions to the Dirichlet problem of the k-Hessian equation. By a g...

Abstract. In this paper, we set up the dynamic frictionless Euler Bernoulli equation with Signorini contact conditions along the length of a thin beam and consider how to solve this equation. The existence of solutions is shown, based on a penalty method. Using energy conservation in the penalty method, we bound the integral of contact forces over time and space. Hölder continuity of the fundam...

In this paper we obtain a Feynman-Kac formula for the solution of a fractional stochastic heat equation driven by fractional noise. One of the main difficulties is to show the exponential integrability of some singular nonlinear functionals of symmetric stable Lévy motion. This difficulty will be overcome by a technique developed in the framework of large deviation. This Feynman-Kac formula is ...

Abstract. We establish existence and pointwise estimates of fundamental solutions and Green’s matrices for divergence form, second order strongly elliptic systems in a domain Ω ⊆ R, n ≥ 3, under the assumption that solutions of the system satisfy De Giorgi-Nash type local Hölder continuity estimates. In particular, our results apply to perturbations of diagonal systems, and thus especially to c...

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lischitz and upper Hölder type, respectively, hold. Furthermore, we apply the a...