In this paper we are concerned with fully nonlinear uniformy elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local Maximum Principle, and their extension up to the boundary. As applications, we deduce ABP type estimates and weak Maximum Principles in general unbounded domains, a strong Maximum principle and a Liouville type t...

The theme of this paper is the extension of continuous valuations on the lattice of open sets of a T0-space to Borel measures. A general extension principle is derived that provides a unified approach to a variety of extension theorems including valuations that are directed suprema of simple valuations, continuous valuations on locally compact sober spaces, and regular valuations on coherent so...

This paper presents an extension of a proof system for encoding generic judgments, the logic FOλ∆∇ of Miller and Tiu, with an induction principle. The logic FOλ∆∇ is itself an extension of intuitionistic logic with fixed points and a “generic quantifier”, ∇, which is used to reason about the dynamics of bindings in object systems encoded in the logic. A previous attempt to extend FOλ∆∇ with an ...

We establish, in innnite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our principle with the extremal principle of Mordukhovich.

This paper presents an extension of a proof system for encoding generic judgments, the logic FOλ∆∇ of Miller and Tiu, with an induction principle. The logic FOλ∆∇ is itself an extension of intuitionistic logic with fixed points and a “generic quantifier”, ∇, which is used to reason about the dynamics of bindings in object systems encoded in the logic. A previous attempt to extend FOλ∆∇ with an ...

Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh’s extension principle, one can obtain a fuzzy extension of any objective function. Computing expensive multivariate functions of fuzzy numbers, however, often poses a difficult problem due to non-applicability of common fuzzy arithmetic algorithms, severe overestimation, or very high computat...

We prove that a nonstandard extension of arithmetic is eeectively conservative over Peano arithmetic by using an internal version of a deenable ultrapower. By the same method we show that a certain extension of the nonstandard theory with a saturation principle has the same proof-theoretic strength as second order arithmetic, where comprehension is restricted to arithmetical formulas.