arXiv subjects

Daniel Maienshein

Publications and source records attributed to Daniel Maienshein.

3 recordsLinked to original sources

arXiv2026

A Classical Analysis Counterpart of Viterbo's Symplectic Geometry Proof of ABP in the Plane

We first provide a classical analysis proof of a version of the Alexandroff-Bakelman-Pucci inequality (ABP) for compactly supported $C^2$ functions in dimension $2$, inspired by the symplectic geometry proof method of Viterbo, which avoids convexity or contact sets. We then show how the proof may be modified to remove the compact support hypothesis and recover the usual statement of ABP, which includes a boundary term. We also discuss the possibility (and difficulties) of extending a pure classical analysis proof to dimension $3$ and above.

math.AP↗

arXiv2025

Quantum Telegraph Behavior Without Photons

We show that a simple model of non-Hermitian noise gives rise to the telegraph switching behavior seen in experiments with single qubits, without any reference to the existence of photons as corpuscles. This lends support to a continuous collapse interpretation of quantum mechanics, but can also be viewed as a model of continuous detection of a steady-state process in the incoherent limit. We show explicitly that such a system obeys the Born rule for particle counting statistics, even though no particle behavior has been invoked at any point in the calculation.

quant-ph↗

arXiv2024

A Compactness Condition for the Theorem of Sums in a Class of Non-Uniformly Elliptic PDEs

In the theory of viscosity solutions for second-order, degenerate elliptic PDEs, the Ishii-Lions method is a commonly used strategy, and the theorem of sums is the main analytical tool. As noted by Porretta and Priola, uniformly elliptic PDEs admit a version of the theorem of sums without the squared term due to a compactness argument. Here, we introduce a larger class of PDEs for which the compactness argument holds.

math.AP↗