Related papers: Improved surrogate bi-parameter maximum principle

In this paper we investigate maximum principles for functionals defined on solutions to special partial differential equations of elliptic type, extending results by Payne and Philippin. We apply such maximum principles to investigate one…

In this note we give an example of measure satisfying the box condition on certain sub-bi-trees (see below) but not satisfying Carleson condition on those sub-bi-trees. This can be considered as a certain counterexample for two weight…

Measurement-constrained datasets, often encountered in semi-supervised learning, arise when data labeling is costly, time-intensive, or hindered by confidentiality or ethical concerns, resulting in a scarcity of labeled data. In certain…

In this survey we formulate our results on different forms of maximum principles for linear elliptic equations and systems. We start with necessary and sufficient conditions for validity of the classical maximum modulus principle for…

We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…

In this paper we develop necessary conditions for optimality, in the form of the stochastic Pontryagin maximum principle, for controlled equation with delay in the state and with control dependent noise, in the general case of controls $u…

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces…

A classical counterexample due to E. De Giorgi, shows that the weak maximum principle does not remain true for general linear elliptic differential systems. After that, there are some efforts to establish the weak maximum principle for…

We provide a proof of strong maximum and minimum principles for fully nonlinear uniformly parabolic equations of second order. The approach is of parabolic nature, slightly differs from the earlier one proposed by L. Nirenberg and does not…

We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a…

We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our…

We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in…

Monadic second order logic can be used to express many classical notions of sets of vertices of a graph as for instance: dominating sets, induced matchings, perfect codes, independent sets or irredundant sets. Bounds on the number of sets…

We consider asynchronous versions of the first and second order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values are chosen a priori. We explore the parameter values that can be…

A proof for the maximum modulus principle (in the unit disc) is presented. This proof is unusual in that it is based on linear algebra.

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…

For an optimal control problem, the concept of a strong local infimum is introduce, for which necessary conditions consisting of some family of "maximum principles" are formulated. If a function delivers a strong local minimum in this…

We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates $V_r$ on $L^p$ spaces for all $1<p<\infty$ and…

We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…

We first prove De Giorgi type level estimates for functions in $W^{1,t}(\Omega)$, $\Omega\subset\mathbb{R}^N$, with $t>N\geq 2$. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not…