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Juan J. Manfredi

Publications and source records attributed to Juan J. Manfredi.

At least 19 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

Superposition Property in Disjoint Variables for the Infinity Laplace Equation

We establish a superposition principle in disjoint variables for the inhomogeneous infinity-Laplace equation. We show that the sum of viscosity solutions of the inhomogeneous infinity-Laplace equation in separate domains is a viscosity solution in the product domain. This result has been used in the literature with certain particular choices of solutions to simplify regularity analysis for a general inhomogeneous infinity-Laplace equation by reducing it to the case without sign-changing inhomogeneous terms and vanishing gradient singularities. We present a proof of this superposition principle for general viscosity solutions. We also explore generalization in metric spaces using cone comparison techniques and study related properties for general elliptic and convex equations.

math.AP↗
arXiv2024

Comparison principles for degenerate sub-elliptic equations in non-divergence form

We prove the comparison principle for viscosity sub/super-solutions of degenerate subelliptic equations in non-divergence form that include the sub-elliptic infinity Laplacian and the normalized p-Laplacian. The equations are defined by a collection of vector fields satisfying Hörmander's rank condition and are left invariant with respect to a nilpotent Lie Group.

math.AP↗
arXiv2021

Design and Characterization of an Optically-Segmented Single Volume Scatter Camera Module

The Optically Segmented Single Volume Scatter Camera (OS-SVSC) aims to image neutron sources for nuclear non-proliferation applications using the kinematic reconstruction of elastic double-scatter events. We report on the design, construction, and calibration of one module of a new prototype. The module includes 16 EJ-204 organic plastic scintillating bars individually wrapped in Teflon tape, each measuring 0.5 cm$\times$0.5 cm$\times$20 cm. The scintillator array is coupled to two custom Silicon Photomultiplier (SiPM) boards consisting of a 2$\times$8 array of SensL J-Series-60035 Silicon Photomultipliers, which are read out by a custom 16 channel DRS-4 based digitizer board. The electrical crosstalk between SiPMs within the electronics chain is measured as 0.76% $\pm$ 0.11% among all 16 channels. We report the detector response of one module including interaction position, time, and energy, using two different optical coupling materials: EJ-560 silicone rubber optical coupling pads and EJ-550 optical coupling grease. We present results in terms of the overall mean and standard deviation of the z-position reconstruction and interaction time resolutions for all 16 bars in the module. We observed the z-position resolution for gamma interactions in the 0.3 MeVee to 0.4 MeVee range to be 2.24 cm$\pm$1.10 cm and 1.45 cm$\pm$0.19 cm for silicone optical coupling pad and optical grease, respectively. The observed interaction time resolution is 265 ps$\pm$29 ps and 235 ps$\pm$10 ps for silicone optical coupling pad and optical grease, respectively.

physics.ins-det↗
arXiv2021

Asymptotic Mean-Value Formulas for Solutions of General Second-Order Elliptic Equations

We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and $k$-Hessian operators.

math.AP↗
arXiv2021

Asymptotic mean value formulas for parabolic nonlinear equations

In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge-Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of Dynamic Programming Principles for certain two-player, zero-sum games.

math.AP↗
arXiv2021

Neutron Response of the EJ-254 Boron-Loaded Plastic Scintillator

Organic scintillators doped with capture agents provide a detectable signal for neutrons over a broad energy range. This work characterizes the fast and slow neutron response of EJ-254, an organic plastic scintillator with 5% natural boron loading by weight. For fast neutrons, the primary mechanism for light generation in organic scintillators is n-p elastic scattering. To study the fast neutron response, the proton light yield of EJ-254 was measured at the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory. Using a broad-spectrum neutron source and a double time-of-flight technique, the EJ-254 proton light yield was obtained over the energy range of approximately 270 keV to 4.5 MeV and determined to be in agreement with other plastic scintillators comprised of the same polymer base. To isolate the slow neutron response, an AmBe source with polyethylene moderator was made incident on the EJ-254 scintillator surrounded by an array of EJ-309 observation detectors. Events in the EJ-254 target coincident with the signature 477.6 keV $γ$ ray (resulting from deexcitation of the residual $^{7}$Li nucleus following boron neutron capture) were identified. Pulse shape discrimination was used to evaluate the temporal differences in the response of EJ-254 scintillation signals arising from $γ$-ray and fast/slow neutron interactions. Clear separation between $γ$-ray and fast neutrons signals was not achieved and the neutron capture feature was observed to overlap both the $γ$-ray and fast neutron bands. Taking into account the electron light nonproportionality, the neutron-capture light yield in EJ-254 was determined to be 89.4$\pm$1.1 keVee.

physics.ins-det↗
arXiv2020

A Nonlinear Mean Value Property for Monge-Ampère

In recent years there has been an increasing interest in whether a mean value property, known to characterize harmonic functions, can be extended in some weak form to solutions of nonlinear equations. This question has been partially motivated by the surprising connection between Random Tug-of-War games and the normalized $p-$Laplacian discovered some years ago, where a nonlinear asymptotic mean value property for solutions of a PDE is related to a dynamic programming principle for an appropriate game. Currently, asymptotic nonlinear mean value formulas are rare in the literature and our goal is to show that an asymptotic nonlinear mean value formula holds for the classical Monge-Ampère equation.

math.AP↗
arXiv2020

Convergence of dynamic programming principles for the $p$-Laplacian

We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.

math.AP↗
arXiv2019

A discrete stochastic interpretation of the Dominative $p$-Laplacian

The Dominative $p$-Laplacian is the operator defined for $2\le p < \infty$ as follows: \begin{equation}\label{dominativep} \mathcal{L}_{p}u(x)=\frac{1}{p}\left(λ_{1}+\ldots+λ_{N-1}\right)+\frac{(p-1)}{p}λ_{N}, \end{equation} where we have ordered the eigenvalues of $D^{2}u(x)$ as $λ_{1}\le λ_{2}\ldots\leλ_{N}$. The operator $\mathcal{L}_{p}u(x)$ was introduced by Brustand to give a natural explanation of the superposition principle for the $p$-Laplace equation. In this paper, we present a discrete stochastic approximation to the unique viscosity solution of the Dirichlet problem for the Dominative $p$-Laplace Equation.

math.AP↗
arXiv2019

Rearrangements in Carnot Groups

In this paper we extend the notion of rearrangement of nonnegative functions to the setting of Carnot groups. We define rearrangement with respect to a given family of anisotropic balls B_r or equivalently with respect to a gauge |x|, and prove basic regularity properties of this construction. If u is a bounded nonnegative real function with compact support, we denote by u* its rearrangement. Then, the radial function u*. is of bounded variation. In addition, if u is continuous then u* is continuous, and if U belongs to the horizontal Sobolev space, we found a generalization of the inequality of Polya and Szegö.

math.AP↗
arXiv2018

$C^{1,α}$-subelliptic regularity on SU(3) and compact, semi-simple Lie groups

Let the vector fields $X_1, ... , X_{6}$ form an orthonormal basis of ${\mathcal H}$, the orthogonal complement of a Cartan subalgebra (of dimension $2$) in SU(3). We prove that weak solutions $u$ to the degenerate subelliptic $p$-Laplacian $$ Δ_{\mathcal{H},{p}} u(x)=\sum_{i=1}^{6} X_i^{*}\left(|\nabla_{\hspace{-0.1cm} {\mathcal H}} u|^{p-2}X_{i}u \right) =0,$$ have Hölder continuous horizontal derivatives $\nabla_{\hspace{-0.1cm}{\mathcal H}} u=(X_1u, \ldots, X_{6}u)$ for $p\ge 2$. We also prove that a similar result holds for all compact connected semisimple Lie groups.

math.AP↗
arXiv2018

Games for Pucci's maximal operators

In this paper we introduce a game whose value functions converge (as a parameter that measures the size of the steps goes to zero) uniformly to solutions to the second order Pucci maximal operators.

math.AP↗
arXiv2015

The obstacle problem for the $p$-laplacian via optimal stopping of Tug-of-War games

We present a probabilistic approach to the obstacle problem for for the $p$-Laplace operator. The solutions are approximated by running processes determined by tug-of-war games plus noise, and letting the step size go to zero, not unlike the case when Brownian motion is approximated by random walks. Rather than stopping the process when the boundary is reached, the value function is obtained by maximizing over all possible stopping times that are smaller than the exit time of the domain.

math.AP↗
arXiv2014

Game Theoretical Methods in Nonlinear PDEs

Nonlinear PDEs, mean value properties, and stochastic differential games are intrinsically connected. In this short expository note, we will describe how the solutions to certain PDEs (of $p$-Laplacian type) can be interpreted as limits of values of a specific Tug-of-War game, when the step-size $ε$ determining the allowed length of move of a token, decreases to $0$.

math.AP↗