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This paper is concerned with two-person dynamic zero-sum games. Let games for some family have common dynamics, running costs and capabilities of players, and let these games differ in densities only. We show that the Dynamic Programming…
This paper is concerned with the Minkowski convolution of viscosity solutions of fully nonlinear parabolic equations. We adopt this convolution to compare viscosity solutions of initial-boundary value problems in different domains. As a…
Aim of this paper is to extend the continuous dependence estimates proved in \cite{JK1} to quasi-monotone systems of fully nonlinear second-order parabolic equations. As by-product of these estimates, we get an H\"older estimate for bounded…
We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial…
Quaternionic Monge-Amp\`{e}re equations have recently been studied intensively using methods from pluripotential theory. We present an alternative approach by using the viscosity methods. We study the viscosity solutions to the Dirichlet…
Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these…
We introduce a concept of asymptotic principal values which enables us to handle rigorously singular integrals of higher-order poles encountered in the computation of various quantities based on correlation functions of a vacuum. Several…
We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.
In this article, we are concerned with a multidimensional degenerate parabolic-hyperbolic equation driven by Levy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous…
In this paper, we prove the pointwise boundary differentiability for viscosity solutions of fully nonlinear elliptic equations. This generalizes the previous related results for linear equations. The geometrical conditions in this paper are…
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
Asymptotic expansion is constructed and justified for the solution to a nonuniform Neumann boundary-value problem for the Poisson equation with the right-hand side that depends both on longitudinal and transversal variables in a thin…
We consider the Cauchy problem for a class of nonlinear degenerate parabolic equa- tion with forcing. By using the vanishing viscosity method we obtain generalized solutions. We prove some regularity results about this generalized…
We consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times. We are dealing with generic situations where the…
We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many…
In this paper, we obtain a stochastic approximation that converges to the viscosity solution of the weighted $p$-Laplace equation. We consider a stochastic two-player zero-sum game controlled by a random walk, two player's choices, and the…
In this work, we study some properties of the viscosity solutions to a degenerate parabolic equation involving the non-homogeneous infinity-Laplacian.
For a family of second-order parabolic systems with rapidly oscillating and time-dependent periodic coefficients, we investigate the asymptotic behavior of fundamental solutions and establish sharp estimates for the remainders.
This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution…
For the system of polyconvex adiabatic thermoelasticity, we define a notion of dissipative measure-valued solution, which can be considered as the limit of a viscosity approximation. We embed the system into a symmetrizable hyperbolic one…