Related papers: ABP maximum principles for fully nonlinear integro…
Results on unconditional convergence in the Maximum norm for ADI-type methods, such as the Douglas method, applied to the time integration of semilinear parabolic problems are quite difficult to get, mainly when the number of space…
We study a class of infinite-horizon average-cost Markov Decision Processes (MDPs) whose reward and transition structures are nearly separable. For the totally separable baseline (that is, with no perturbation), we derive an explicit…
We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains $\Omega \subset \mathbb R^n$ of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…
This paper presents the development and analysis of an asymptotically compatible (AC) unfitted finite element method for one-dimensional nonlocal elliptic interface problems. The proposed method achieves optimal error estimates through…
The Bregman proximal gradient method (BPGM), which uses the Bregman distance as a proximity measure in the iterative scheme, has recently been re-developed for minimizing convex composite problems without the global Lipschitz gradient…
The Borichev--Tomilov theorem \cite{BT2010} provides a sharp characterization of polynomial decay for linear $C_0$-semigroups in terms of resolvent growth along the imaginary axis. In the nonlinear setting, the absence of a spectral theory…
We give full boundary extensions to two fundamental estimates in the theory of elliptic PDE, the weak Harnack inequality and the quantitative strong maximum principle, for uniformly elliptic equations in non-divergence form.
We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge-Amp\`{e}re equation. We prove an ABP estimate and a Harnack inequality and derive H\"{o}lder and…
It is well known that the classic Allen-Cahn equation satisfies the maximum bound principle (MBP), that is, the absolute value of its solution is uniformly bounded for all time by certain constant under suitable initial and boundary…
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result…
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of…
This work addresses the problem of (global) maximal regularity for quasilinear evolution equations with sublinear gradient growth and right-hand side in Lebesgue spaces, complemented with Neumann boundary conditions. The proof relies on a…
The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori error estimates of optimal order under optimal regularity…
In this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin's maximum principle from optimal control theory for the Loewner equation in several complex…
Physical solutions to the widely used Aw-Rascle-Zhang (ARZ) traffic model and the adapted pressure (AP) ARZ model should satisfy the positivity of density, the minimum and maximum principles with respect to the velocity $v$ and other…
We consider the setting of two disks in a domain in $\mathbb{R}^2$ which are almost touching and have finite and positive conductivities, giving rise to a divergence form elliptic equation with discontinuous coefficients. We use the maximum…
In this paper, we investigate the maximum number of limit cycles of the reduced Abel equation $\dot{x}=A(t)x^{3}+B(t)x^{2}$ on an interval $[0,T]$. The Smale-Pugh problem asks whether this maximum number is bounded in terms of a given class…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the…