3 citations · 5 across the 5 of their papers we have counts for
9 papers
Aleksandrov-Bakelman-Pucci maximum principle for -viscosity solutions of uniformly elliptic equations with unbounded terms: The critical case
Andrzej Święch
We prove the Aleksandrov-Bakelman-Pucci maximum principle for -viscosity sub/super-solutions of fully nonlinear uniformly elliptic equations in with the…
Existence of solutions to a fully nonlinear free transmission problem
Edgard A. Pimentel, Andrzej Święch
We study an equation governed by a discontinuous fully nonlinear operator. Such discontinuities are solution-dependent, which introduces a free boundary. Working under natural assu…
A fully nonlinear degenerate free transmission problem
Gerardo Huaroto, Edgard A. Pimentel, Giane C. Rampasso +1
We study a free transmission problem driven by degenerate fully nonlinear operators. Our first result concerns the existence of solutions to the associated Dirichlet problem. By fr…
Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications
Shigeaki Koike, Andrzej Swiech, Shota Tateyama
The weak Harnack inequality for -viscosity supersolutions of fully nonlinear second-order uniformly parabolic partial differential equations with unbounded coefficients and in…
Coupling Levy measures and comparison principles for viscosity solutions
Nestor Guillen, Chenchen Mou, Andrzej Swiech
We prove new comparison principles for viscosity solutions of non-linear integro-differential equations. The operators to which the method applies include but are not limited to th…
Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations
Ruoting Gong, Chenchen Mou, Andrzej Swiech
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differ…
Partial regularity of viscosity solutions for a class of Kolmogorov equations arising from mathematical finance
Mauro Rosestolato, Andrzej Świech
We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are regular on special finite dimensional…
Scaling limits for conditional diffusion exit problems, Doob's h-transform, and asymptotics for nonlinear elliptic equations
Yuri Bakhtin, Andrzej Swiech
The goal of this paper is to supplement the large deviation principle of the Freidlin--Wentzell theory on exit problems for diffusion processes with results of classical central li…
Large deviations for stochastic PDE with Levy noise
Andrzej Swiech, Jerzy Zabczyk
We prove a large deviation principle result for solutions of abstract stochastic evolution equations perturbed by small Levy noise. We use general large deviations theorems of Vara…