Related papers: The Parabolic Infinite-Laplace Equation in Carnot …

We study the Cauchy problem for the parabolic infinity Laplace equation. We prove a new comparison principle and obtain uniqueness of viscosity solutions in the class of functions with a polinomial growth at infinity, improving previous…

In this paper, we establish the properties of viscosity solutions in Martinet spaces, which lack both the algebraic group law of Carnot groups and the triangular vector fields of Grushin-type spaces. We then prove the uniqueness of…

In this manuscript, we prove existence of viscosity solutions to singular parabolic equations in Carnot groups. We develop the analysis by constructing appropriate deterministic games adapted to the algebraic and differential structures of…

In this paper we prove a strong maximum principle for certain parabolic systems of equations. In particular, our methods place no restriction on the regularity of the boundary of the convex set in which the system takes its values, and…

The stability for the viscosity solutions of a differential equation with a perturbation term added to the Infinity-Laplace Operator is studied. This is the so-called Infinity-Laplace Equation with variable exponent infinity. An…

For any Carnot group $\bf G$ and a bounded domain $\Omega\subset \bf G$, we prove that viscosity solutions in $C(\bar\Om)$ of the fully nonlinear subelliptic equation $F(u,\nabla_h u, \nabla^2_h u)=0$ are unique when $F\in C(R\times…

We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points. These are characteristic points for the level sets of 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…

We prove the uniqueness for viscosity solutions of a differential equation involving the infinity-Laplacian with a variable exponent. A version of the Harnack's inequality is derived for this minimax problem.

In this article we present several results concerning uniqueness of $C$-viscosity and $L_{p}$-viscosity solutions for fully nonlinear parabolic equations. In case of the Isaacs equations we allow lower order terms to have just measurable…

In this work, we study some properties of the viscosity solutions to a degenerate parabolic equation involving the non-homogeneous infinity-Laplacian.

We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are…

We show how a theorem about the solvability in $W^{1,2}_{\infty}$ of special parabolic Isaacs equations can be used to obtain the existence and uniqueness of viscosity solutions of general uniformly nondegenerate parabolic Isaacs equations.…

In this paper, we show the existence and uniqueness of viscosity solution to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations. This extends recent results of Eyssidieux-Guedj-Zeriahi.

We prove a result of existence of regular solutions and a maximum principle for solutions to a parabolic p-Laplacian system with convective term.

We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampere-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for…

We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem $u_t = \Delta_\infty^h u$ where $\Delta_\infty^h$ is the $h$-homogeneous operator associated with the infinity-Laplacian, $\Delta_\infty^h u =…

We prove for the $N$-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level $h>0$ of the motion can also be chosen arbitrarily. Our approach is…

In this paper we show that the maximal viscosity solution of a class of quasi-convex Hamilton--Jacobi equations, coupled with inequality constraints on the boundary, can be recovered by taking the limit as $p\to\infty$ in a family of…

We obtain new oscillation and gradient bounds for the viscosity solutions of fully nonlinear degenerate elliptic equations where the Hamiltonian is a sum of a sublinear and a superlinear part in the sense of Barles and Souganidis (2001). We…