Related papers: A viscosity approach to the Dirichlet problem for …
In this paper, we propose a Cauchy type problem to the timelike Lorentzian eikonal equation on a globally hyperbolic space-time. For this equation, as the value of the solution on a Cauchy surface is known, we prove the existence of…
We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity…
In this work, we study some properties of the viscosity solutions to a degenerate parabolic equation involving the non-homogeneous infinity-Laplacian.
We study the Dirichlet problem for subelliptic partial differential equations of Monge-Ampere type involving the derivates with respect to a family X of vector fields of Carnot type. The main result is a comparison principle among viscosity…
This paper is concerned with semiconcavity of viscosity solutions for a class of degenerate elliptic integro-differential equations in $\mathbb R^n$. This class of equations includes Bellman equations containing operators of L\'evy-It\^o…
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique…
In this paper we study the Dirichlet problem for a class of Hessian type equation with its structure as a combination of elementary symmetric functions on Hermitian manifolds. Under some conditions with the initial data on manifolds and…
We introduce a notion of viscosity solutions for a nonlinear degenerate diffusion equation with a drift potential. We show that our notion of solutions coincide with the weak solutions defined via integration by parts. As an application of…
In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations is considered. When viscosity coefficients are given as a constant multiple of the density's power ($\rho^\delta$ with…
In this paper, we consider the Dirichlet problem for a class of prescribed Hessian quotient type curvature equations with homogeneous boundary data in Minkowski space. By establishing the a priori C2 estimates, we obtain the existence…
We prove regularity results such as interior Lipschitz regularity and boundary continuity for the Cauchy-Dirichlet problem associated to a class of parabolic equations inspired by the evolutionary $p$-Laplacian, but extending it at a wide…
We establish the interior $C^{1,\alpha}$-estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations $$u_t = |Du|^{\gamma}F(D^2u) + f.$$ For this purpose, we prove the well-posedness of the regularized…
In this paper, we study a class of special Lagrangian curvature potential equations and obtain the existence of smooth solutions for Dirichlet problem. The existence result is based on a priori estimates of global $C^{0}$, $C^{1}$ and…
We prove smoothness and interior derivative estimates for viscosity solutions to the special Lagrangian equation with almost negative phases and small enough semi-convexity. We show by example that the range of phases we consider and the…
We give a proof of existence and uniqueness of viscosity solutions to parabolic quasilinear equations for a fairly general class of nonconvex Hamiltonians with superlinear growth in the gradient variable. The approach is mainly based on…
In this paper, we establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for Hessian quotient equations with prescribed asymptotic behavior at infinity. This extends the previous related results on…
In this article, we are interested in the Dirichlet problem for parabolic viscous Hamilton-Jacobi Equations. It is well-known that the gradient of the solution may blow up in finite time on the boundary of the domain, preventing a classical…
We consider the Dirichlet problem for two types of degenerate elliptic Hessian equations . New results about solvability of the equations in the $C^{1,1}$ space are provided.
In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients and a term of capillarity introduced by Coquel et al in \cite{5CR}. This model includes at the same time the barotropic…
The Monge-Amp\`ere type equations over bounded convex domains arise in a host of geometric applications. In this paper, we focus on the Dirichlet problem for a class of Monge-Amp\`ere type equations, which can be degenerate or singular near…