Related papers: On sharp Agmon-Miranda maximum principles

We consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the one-dimensional case we classify all bounded steady states…

A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…

We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set $P$ and…

This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…

Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…

We obtain new local Calderon-Zygmund estimates for elliptic equations with matrix-valued weights for linear as well as non-linear equations. We introduce a novel log-BMO condition on the weight M. In particular, we assume smallness of the…

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…

The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma…

In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a…

This paper deals with explicit upper and lower bounds for principal eigenvalues and the maximum principle associated to generalized Lane-Emden systems (GLE systems, for short). Regarding the bounds, we generalize the upper estimate of…

This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…

There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…

We give a quick and direct proof of the strong maximum principle on finite dimensional $RCD$ spaces based on the Laplacian comparison of the squared distance.

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…

We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…

We establish optimal, quantitative H\"oder estimates for the gradient of solutions to a class of degenerate elliptic equations with Hamiltonian terms. The presence of such lower-order terms introduces additional challenges, particularly in…

We give a unified approach to strong maximum principles for a large class of nonlocal operators of the order $s\in(0,1)$, that includes the Dirichlet, the Neumann Restricted (or Regional) and the Neumann Semirestricted Laplacians.

Using three different notions of generalized principal eigenvalue of linear second order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the…

This work studies a class of non-smooth decentralized multi-agent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common non-smooth term. We propose a general primal-dual…

Discrete maximum principles in the approximation of partial differential equations are crucial for the preservation of qualitative properties of physical models. In this work we enforce the discrete maximum principle by performing a simple…