Search results for "35"
showing 10 items of 2413 documents
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 .
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.
Fractional Hardy inequalities and visibility of the boundary
2013
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.
A Comparative Eye Tracking Study of Usability—Towards Sustainable Web Design
2021
Websites are one of the most frequently used communication environments, and creating sustainable web designs should be an objective for all companies. Ensuring high usability is proving to be one of the main contributors to sustainable web design, reducing usage time, eliminating frustration and increasing satisfaction and retention. The present paper studies the usability of different website landing pages, seeking to identify the elements, structures and designs that increase usability. The study analyzed the behavior of 22 participants during their interaction with five different landing pages while they performed three tasks on the webpage and freely viewed each page for one minute. Th…
The role of the agreement as a tool for management of property relations in cases of cross border marriages and civil unions/partnerships registered …
2021
The essay examines the role of the agreement as a tool for managing property relationships in crossborder marriages and registered partnerships, in light of EU Regulations 1103 and 1104 of 2016, on the property regimes of international married or registered couples. The main prerogative of such acts is the recognition of the parties? freedom to choose the court and the applicable law. The law governing the matrimonial property regimes, or the property consequences of registered partnerships, has universal scope. This agreement in the form envisaged, which is backed by the need for legal certainty and predictability of the applicable rules, means that the spouses, in family problems which ha…
The MIMOSE Approach to Support Sustainable Forest Management Planning at Regional Scale in Mediterranean Contexts
2017
In recent decades, Mediterranean landscapes have been affected by human-induced drivers, such as land use and climate change. Forest ecosystems and landscapes have been particularly affected in mountainous regions due to limited management and stewardship, especially in remote areas. Therefore, there is a need to set up new strategies to enhance ecosystem services in forested areas which, in turn, will benefit local communities and economies. In this study, we implemented a new approach—Multiscale Mapping of Ecosystem Services (MIMOSE)—to assess ecosystem services in Mediterranean forests located in a mountainous region of Italy. We spatially assessed timber provision and carbon sequestrati…
The Relationship between Knowledge Characteristics’ Fit and Job Satisfaction and Job Performance: The Mediating Role of Work Engagement
2020
Knowledge workers are highly valued by organizations, but there is a lack of evidence about the role of work engagement in the satisfaction and performance of these workers. Harmonization and Person&ndash
Inspiriting Innovation: The Effects of Leader-Member Exchange (LMX) on Innovative Behavior as Mediated by Mindfulness and Work Engagement
2021
Continuous innovation has become a key to gaining a sustainable competitive advantage for organizations in the 21st century. By focusing on the underlying mechanisms (i.e., mindfulness and work engagement) by which it works, this study addresses the quality of leader–member relationships and their relevance for innovation in the workplace. Using a sample of 210 employees from 17 Spanish companies, a two-wave longitudinal design evaluated the mediational roles of mindfulness and engagement between leader–member exchange (LMX) quality and innovative work behavior (IWB) in an organizational context. Over the course of a year, two questionnaires were administered to measure LMX quality, mindful…