Related papers: Improved surrogate bi-parameter maximum principle

In this paper, we prove a maximum principle for the $p$-Laplacian with a sign-changing weight. As an application of this maximum principle, we study the existence of one-sign solutions for a class of quasilinear elliptic problems.

Let M denote the maximal function along the polynomial curve p(t)=(t,t^2,...,t^d) in R^d: M(f)=sup_{r>0} (1/2r) \int_{|t|<r} |f(x-p(t))| dt. We show that the L^2-norm of this operator grows at most logarithmically with the parameter d:…

We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result to both classical and intuitionistic linear logic as well…

This note defines a notion of multiplicity for nodes in a rooted tree and presents an asymptotic calculation of the maximum multiplicity over all leaves in a Bienaym\'e-Galton-Watson tree with critical offspring distribution $\xi$,…

We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint…

The problem of maximizing precision at the top of a ranked list, often dubbed Precision@k (prec@k), finds relevance in myriad learning applications such as ranking, multi-label classification, and learning with severe label imbalance.…

In this note we give a proof-by-formula of certain important embedding inequalities on dyadic tree. This is done with the help of Bellman function. We also consider the case of a bi-tree, where a different approach is explained.

The purpose of this survey is to present analytic versions of the injectivity theorem and their applications. The proof of our injectivity theorems is based on a combination of the L^2-method for the dbar-equation and the theory of harmonic…

In this paper we develop a detailed study on maximum and comparison principles for a degenerate elliptic system. Explicit lower bounds for principal eigenvalues of this system in terms of the measure of $\Omega$ are also proved.

We present a version of the stochastic maximum principle (SMP) for ergodic control problems. In particular we give necessary (and sufficient) conditions for optimality for controlled dissipative systems in finite dimensions. The strategy we…

We prove the sufficiency of the Linear Superposition Principle for linear trees, which characterizes the spectra achievable by a real symmetric matrix whose underlying graph is a linear tree. The necessity was previously proven in 2014.…

We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of $\mathbb{R}^n$. The simplicity and robustness of our maximum principle-based argument provides for its…

The work continues the author's many-year research in theory of maximal branching processes, which are obtained from classical branching processes by replacing the summation of descendant numbers with taking the maximum. One can say that in…

We argue that the spiral can, in presence of a maximum principle, be of maximal rank at a boundary, but does not preserve hypoellipticity.

In this paper we consider a measure-theoretical formulation of the training of NeurODEs in the form of a mean-field optimal control with $L^2$-regularization of the control. We derive first order optimality conditions for the NeurODE…

We provide an improvment of the maximum principle of Pon-tryagin of the optimal control problems, for a system governed by an ordinary differential equation, in presence of final constraints, in the setting of the piece-wise differentiable…

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…

The maximum volume principle is investigated as a means to solve the following problem: Given a set of arbitrary interpolation nodes, how to choose a set of polynomial basis functions for which the Lagrange interpolation problem is…

We show that the maximal linear extension theorem for well partial orders is equivalent over RCA_0 to ATR_0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR_0 over RCA_0.

In this paper, we consider stochastic control problems on the Sierpinski gasket. An order comparison lemma is derived using heat kernel estimate for Brownian motion on the gasket. Using the order comparison lemma and techniques of BSDEs, we…