Related papers: Strong Comparison Principles for Some Nonlinear De…

This paper proves comparison principles for elliptic PDE involving the Finsler infinity Laplacian, a second-order differential operator with discontinuities in the gradient variable arising in $L^{\infty}$-variational problems and…

We establish a priori regularity estimates for viscosity solutions of degenerate fully nonlinear elliptic equations with integrable right-hand sides. When the nonhomogeneous term belongs to $L^p$ with $p>n$, we prove optimal interior…

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…

We obtain an error estimate between viscosity solutions and \delta-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides uniform ellipticity, is that the nonlinearity is…

For scalar fully nonlinear partial differential equations depending on the Hessian andspatial coordinates, we present a general theory for obtaining comparison principles and well posedness for the associated Dirichlet problem with…

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

We investigate strong maximum (and minimum) principles for fully nonlinear second order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of…

We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by \begin{equation*} \begin{cases} \displaystyle -\Delta_p u= \frac{f}{u^\gamma} + g u^q & \mbox{in $\Omega$,} \\ u = 0 & \mbox{on…

In this article, we study nonlinear nonlocal equations with coercive gradient nonlinearity of the form \[ (-\Delta_p)^s u(x) + H(x, \nabla u) = f, \] where $f$ is Lipschitz continuous. We show that any viscosity solution $u$ is locally…

In this paper, we study some properties of viscosity sub/super-solutions of a class of fully nonlinear elliptic equations relative to the eigenvalues of the complex Hessian. We show that every viscosity subsolution is approximated by a…

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…

This paper is devoted to the quantitative homogenization of multiscale elliptic operator $-\nabla\cdot A_\varepsilon \nabla$, where $A_\varepsilon(x) = A(x/\varepsilon_1, x/\varepsilon_2,\cdots, x/\varepsilon_n)$, $\varepsilon =…

We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to $Du$. We prove several comparison principles among viscosity solutions which may be unbounded…

We develop a new, unified approach to the following two classical questions on elliptic PDE: the strong maximum principle for equations with non-Lipschitz nonlinearities, and the at most exponential decay of solutions in the whole space or…

We consider weak solutions to $$-\Delta_pu+a(x,u)|\nabla u|^q=f(x,u),$$ with $p>1$, $q\geq\max\,\{p-1,1\}$. We exploit the Moser iteration technique to prove a Harnack comparison inequality for $C^1$ weak solutions. As a consequence we…

We study a singular elliptic problem driven by a mixed local-nonlocal operator of the form \begin{equation*} \begin{aligned} -\Delta_p u + (-\Delta_q)^s u &= \frac{\lambda}{u^{\delta}} + u^r \text{ in } \Omega\newline u > 0 \text{ in }…

We address some regularity issues for mixed local-nonlocal quasilinear operators modeled upon the sum of a $p$-Laplacian and of a fractional $(s, q)$-Laplacian. Under suitable assumptions on the right-hand sides and the outer data, we show…

Let $\Omega$ be a Lipschitz domain in $\mathbb R^d$, and let $\mathcal A^\varepsilon=-\operatorname{div}A(x,x/\varepsilon)\nabla$ be a strongly elliptic operator on $\Omega$. We suppose that $\varepsilon$ is small and the function $A$ is…

In this article we prove some Lipschitz estimates and existence result for a class of degenerate fully nonlinear elliptic equations which are a generalization of the pseudo p-Laplacian. The operators are degenerate elliptic at any point…

We start presenting an $L^{\infty}$-gradient bound for solutions to non-homogeneous $p$-Laplacean type systems and equations, via suitable non-linear potentials of the right hand side. Such a bound implies a Lorentz space characterization…