Search results for "DIF"

Game-Theoretic Approach to Hölder Regularity for PDEs Involving Eigenvalues of the Hessian

2021

AbstractWe prove a local Hölder estimate for any exponent $0<\delta <\frac {1}{2}$ 0 < δ < 1 2 for solutions of the dynamic programming principle $$ \begin{array}{@{}rcl@{}} u^{\varepsilon} (x) = \sum\limits_{j=1}^{n} \alpha_{j} \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2} \end{array} $$ u ε ( x ) = ∑ j = 1 n α j inf dim ( S ) = j sup v ∈ S | v | = 1 u ε ( x + ε v ) + u ε ( x − ε v ) 2 with α1,αn > 0 and α2,⋯ ,αn− 1 ≥ 0. The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE $…

Equivalence of viscosity and weak solutions for a $p$-parabolic equation

2019

AbstractWe study the relationship of viscosity and weak solutions to the equation $$\begin{aligned} \smash {\partial _{t}u-\varDelta _{p}u=f(Du)}, \end{aligned}$$ ∂ t u - Δ p u = f ( D u ) , where $$p>1$$ p > 1 and $$f\in C({\mathbb {R}}^{N})$$ f ∈ C ( R N ) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when $$p\ge 2$$ p ≥ 2 .

Hölder gradient regularity for the inhomogeneous normalized p(x)-Laplace equation

2022

We prove the local gradient Hölder regularity of viscosity solutions to the inhomogeneous normalized p(x)-Laplace equation −Δp(x)Nu=f(x), where p is Lipschitz continuous, inf⁡p>1, and f is continuous and bounded. peerReviewed

Regularity for nonlinear stochastic games

2015

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed

Remarks on regularity for p-Laplacian type equations in non-divergence form

2018

We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.

Dzimuma loma valodas lietojumā lietišķajās prezentācijās

2018

Šajā bakalaura darbā tiek pētīta dzimumu loma valodu lietojumā lietišķajās prezentācijās, jo mūsdienu sabiedrībā cilvēkiem tagad ir jārunā publiski vairāk nekā jebkad agrāk. Bakalaura darba mērķis ir izpētīt, kā valodas lietojumu lietišķajās prezentācijās ietekmē runātāja dzimums. Autore ir pētījusi vairākus teorētiskos avotus par komunikāciju, lietišķajām prezentācijām un dzimuma atšķirībām runā. Autore ir izpētījusi piecas vīriešu un piecas sieviešu ar uzņēmējdarbību saistītas prezentācijas. Lai analizētu atšķirības starp vīriešu un sieviešu valodas lietojumu izvēlētajās lietišķajās prezentācijās, tiek izmantota kvalitatīva gadījumu izpētes pieeja. Tiek secināts, ka valodas lietojumu liet…

Lidar detection of carbon dioxide in volcanic plumes

2015

Volcanic gases give information on magmatic processes. In particular, anomalous releases of carbon dioxide precede volcanic eruptions. Up to now, this gas has been measured in volcanic plumes with conventional measurements that imply the severe risks of local sampling and can last many hours. For these reasons and for the great advantages of laser sensing, the thorough development of volcanic lidar has been undertaken at the Diagnostics and Metrology Laboratory (UTAPRAD-DIM) of the Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA). In fact, lidar profiling allows one to scan remotely volcanic plumes in a fast and continuous way, and with high s…

Volcanic Plume CO2 Flux Measurements at Mount Etna by Mobile Differential Absorption Lidar

2017

Volcanic eruptions are often preceded by precursory increases in the volcanic carbon dioxide (CO2) flux. Unfortunately, the traditional techniques used to measure volcanic CO2 require near-vent, in situ plume measurements that are potentially hazardous for operators and expose instruments to extreme conditions. To overcome these limitations, the project BRIDGE (BRIDging the gap between Gas Emissions and geophysical observations at active volcanoes) received funding from the European Research Council, with the objective to develop a new generation of volcanic gas sensing instruments, including a novel DIAL-Lidar (Differential Absorption Light Detection and Ranging) for remote (e.g., distal) …

Relationship between volume and energy of vector fields

2001

Abstract A unified study of energy and volume functionals is presented here by determining the critical points of a functional that extends simultaneously energy and volume and that is defined on the product of the manifold of smooth maps C∞(M,N) times the manifold M of riemannian metrics on M. The restriction of this functional to different submanifolds of the space of vector fields X (M)× M is also considered, and used to study several functionals generalizing volume and energy or total bending of vector fields

Verkostot, paikallisuus ja eriarvoisuus

2012