Related papers: Constrained energy problems with external fields
As explained in detail in the prologue to this manuscript, boundedness of weak solutions for general classes of elliptic equations in divergence form is a classic tool for achieving higher regularity. We propose here some global boundedness…
Optimal control problems without control costs in general do not possess solutions due to the lack of coercivity. However, unilateral constraints together with the assumption of existence of strictly positive solutions of a pre-adjoint…
We provide new general kernel selection rules thanks to penalized least-squares criteria. We derive optimal oracle inequalities using adequate concentration tools. We also investigate the problem of minimal penalty as described in [BM07].
Low-energy tests of fundamental symmetries and studies of neutrino properties provide a powerful window on physics beyond the Standard Model (BSM). In this article, we provide a basic theoretical framework for a subsequent set of articles…
We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a…
This paper initiates a program which seeks to study the allowed spatial distributions of negative energy density in quantum field theory. Here we deal with free fields in Minkowski spacetime. Known restrictions on time integrals of the…
It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…
This paper provides a new theoretical lens for understanding the finite-sample performance of kernel-based specification tests, such as the Kernel Conditional Moment (KCM) test. Rather than introducing a fundamentally new test, we isolate…
We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric graphs, several new features appear, such as the existence…
We prove existence and uniqueness of solutions to a class of porous media equations driven by the fractional Laplacian when the initial data are positive finite Radon measures on the Euclidean space. For given solutions without a prescribed…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
We consider aggregation-diffusion equations with merely bounded nonlocal interaction potential $K$. We are interested in establishing their well-posedness theory when the nonlocal interaction potential $K$ is neither differentiable nor…
Positive semi-definite kernels are used to induce pseudo-metrics, or ``distances'', between measures. We write these as an expected quadratic variation of, or expected inner product between, a random field and the difference of measures.…
We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of…
We consider Kaluza-Klein models where internal spaces are compact flat or curved Einstein spaces. This background is perturbed by a compact gravitating body with the dust-like equation of state (EoS) in the external/our space and an…
The latest cosmological constraints on the sum of the neutrino masses depend on prior physical assumptions about the mass spectrum. To test the accordance of cosmological and laboratory constraints in the absence of such priors, we…
We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…
QFT with an external background can be considered as a consistent model only if backreaction is relatively small with respect to the background. To find the corresponding consistency restrictions on an external electric field and its…
This study seeks a better comprehension of anomalies by exploring (n+1)-point perturbative amplitudes in a 2n-dimensional framework. The involved structures combine axial and vector vertices into odd tensors. This configuration enables…
We study functions of least gradient as well as related superminimizers and solutions of obstacle problems in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show a standard weak Harnack…