Integral maximum principle and its applications

Maximum Principle for Spdes and Its Applications

The maximum principle for SPDEs is established in multidimensional C domains. An application is given to proving the Hölder continuity up to the boundary of solutions of one-dimensional SPDEs. The maximum principle is one of the most powerful tools in the theory of second-order elliptic and parabolic partial differential equations. However, until now it did not play any significant role in the ...

Multitime maximum principle for curvilinear integral cost

Recently we have created a multitime maximum principle gathering together some concepts in Mechanics, Field Theory, Differential Geometry, and Control Theory. The basic tools of our theory are variational PDE systems, adjoint PDE systems, Hamiltonian PDE systems, duality, multitime maximum principle, incavity on manifolds etc. Now we justify the multitime maximum principle for curvilinear integ...

A Maximum Principle for Stochastic Optimal Control with Terminal State Constraints, and Its Applications

This paper is concerned with a stochastic optimal control problem where the controlled system is described by a forward–backward stochastic differential equation (FBSDE), while the forward state is constrained in a convex set at the terminal time. An equivalent backward control problem is introduced. By using Ekeland’s variational principle, a stochastic maximum principle is obtained. Applicati...

The Maximum Entropy Production Principle: Its Theoretical Foundations and Applications to the Earth System

The Maximum Entropy Production (MEP) principle has been remarkably successful in producing accurate predictions for non-equilibrium states. We argue that this is because the MEP principle is an effective inference procedure that produces the best predictions from the available information. Since all Earth system processes are subject to the conservation of energy, mass and momentum, we argue th...

An Integral Inequality and Its Applications