Related papers: Comparison principles for degenerate sub-elliptic …

The validity of the comparison principle in variable coefficient fully nonlinear gradient free potential theory is examined and then used to prove the comparison principle for fully nonlinear partial differential equations which determine a…

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…

We consider nonlinear elliptic equations of the $p$-Laplacian type with lower order terms which involve nonnegative potentials satisfying a reverse H\"older type condition. Then we obtain interior and boundary $L^q$ estimates for the…

We present comparison principles, Lipschitz estimates and study state constraints problems for degenerate, second-order Hamilton-Jacobi equations.

We prove H\"older estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional $p$-Laplace equation $$ \text{PV}…

For each $k = 0,\dots,n$ we construct a continuous phase $f_k$, with $f_k(0) = (n-2k)\frac{\pi}{2}$, and viscosity sub- and supersolutions $v_k$, $u_k$, of the elliptic PDE $\sum_{i=1}^n \arctan(\lambda_i(D^2 w)) = f_k(x)$ such that…

We prove a comparison result for viscosity solutions of (possibly degenerate) parabolic fully nonlinear path-dependent PDEs. In contrast with the previous result in Ekren, Touzi & Zhang, our conditions are easier to check and allow for the…

We establish the equivalence between the notions of weak and viscosity solutions for non-homogeneous equations whose main operator is the fractional p-Laplacian and the lower order term depends on $x$, $u$ and $D_s^p u$, being the last one…

This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test function framework, that allows for the simultaneous…

Denote by $\Delta$ the Laplacian and by $\Delta_\infty $ the $\infty$-Laplacian. A fundamental inequality is proved for the algebraic structure of $\Delta v\Delta_\infty v$: for every $v\in C^\infty$, $$\ | { |D^2vDv|^2} - {\Delta v…

In this work, we establish global gradient estimates to solutions of quasilinear elliptic models in non-divergence form with general degeneracy law and a Hamiltonian term, given by $$ -\Psi(x, |\nabla…

We study a class of linear parabolic equations in divergence form with degenerate coefficients on the upper half space. Specifically, the equations are considered in $(-\infty, T) \times \mathbb{R}^d_+$, where $\mathbb{R}^d_+ = \{x \in…

We prove global comparison results for the $p$-Laplacian on a $p$-parabolic manifold. These involve both real-valued and vector-valued maps with finite $p$-energy.

We prove an existence result for solutions to a class of nonlinear degenerate-elliptic equations with measurable coefficients and zero Dirichlet boundary condition. The main term is given by a nonlinear operator in divergence form…

In this article, we prove the uniqueness of viscosity solutions to $\mathcal{L}_{\infty} u =f$ in $\Omega$, where $\mathcal{L}_{\infty}$ denotes the nonlocal infinity Laplace operator, $\Omega$ a bounded domain, and $f$ a continuous…

In this article, we are interested in semilinear, possibly degenerate elliptic equations posed on a general network, with nonlinear Kirchhoff-type conditions for its interior vertices and Dirichlet boundary conditions for the boundary ones.…

We investigate strong and weak versions of maximum and comparison principles for a class of quasilinear parabolic equations with the $p$-Laplacian $$ \partial_t u - \Delta_p u = \lambda |u|^{p-2} u + f(x,t) $$ under zero boundary and…

We analyze $p$-Laplace operators with degenerate elliptic coefficients. This investigation includes Gru\v{s}in type $p$-Laplace operators. We describe a \emph{separation phenomenon} in elliptic and parabolic $p$-Laplace type equations,…

We prove existence and uniqueness results of positive viscosity solutions of fully nonlinear degenerate elliptic equations with power-like zero order perturbations in bounded domains. The principal part of such equations is either…

We establish the comparison principle, existence and regularity of viscosity solutions to the following problem concerning the mixed operator: \begin{align} \begin{cases}…