A Dirichlet Problem in Noncommutative Potential Theory

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

Brelops Axiomatic Theory of the Dirichlet Problem and Hunt's Theory

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A Noncommutative Enumeration Problem

Quantum Theory, Noncommutative Gravity, and the Cosmological Constant Problem

The cosmological constant problem is principally concerned with trying to understand how the zeropoint energy of quantum fields contributes to gravity. Here we take the approach that by addressing a fundamental unresolved issue in quantum theory we can gain a better understanding of the problem. Our starting point is the observation that the notion of classical time is external to quantum mecha...

A Dirichlet Problem in the Strip

In this paper we investigate a Dirichlet problem in a strip and, using the sliding method, we prove monotonicity for positive and bounded solutions. We obtain uniqueness of the solution and show that this solution is a function of only one variable. From these qualitative properties we deduce existence of a classical solution for this problem.