Search results for "PSC"
showing 10 items of 183 documents
Existence and classification of critical points for nondifferentiable functions
2004
A general min-max principle established by Ghoussoub is extended to the case of functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. Some topological properties of the min-max-generated critical points in such a framework are then pointed out.
Solvability of a first order system in three-dimensional non-smooth domains
1985
summary:A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain $\Omega\subset \bold R^3$. On the boundary $\delta\Omega$, the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.
Two examples related to conical energies
2022
In a recent article we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces of Lipschitz graphs, and a sufficient condition for boundedness of nice singular integral operators. In this note we give two examples related to sharpness of these results. One of them is due to Joyce and M\"{o}rters, the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.
ICT for external use in Croatian four- and five-star hotels
2016
The Purpose – The objective of the paper is to examine the implementation of advanced technology and promotional supports in hotel companies and to compare their performance in four- and five-star hotels. More specifically, ICT for external use are analysed, i.e. customer relationship management (CRM), communication with customers, promotional supports, and online order receptions. Design/Methodology/Approach – The empirical research took place in 38 upscale (26 four and 12 five-star) hotels located in Croatia, in the regions of Dalmatia, Istria, and Kvarner, and in the city of Zagreb. The data were collected through a structured questionnaire administered mainly during personal interviews …
Precursors of bipolar disorders: A systematic literature review of prospective studies
2015
Objective To evaluate the presence of affective signs and symptoms as precursors of bipolar disorder in prospective studies, including assessment of their prevalence, duration, and predictive value. Data sources We followed PRISMA guidelines to search PubMed, CINAHL, PsycINFO, EMBASE, SCOPUS, and ISI Web of Science databases to May 31, 2013, using the terms bipolar disorder AND (antecedent* OR predict* OR prodrom* OR prospect*) AND (diagnosis OR development). Hand searching of identified reports led to additional relevant references. Study selection We included only English-language articles containing (1) prospective, longitudinal studies with at least 2 structured clinical assessments (in…
Musculoskeletal examination in young athletes and non-athletes:the Finnish Health Promoting Sports Club (FHPSC) study
2018
ObjectivesTo determine the inter-rater repeatability of a musculoskeletal examination and to compare findings between adolescent athletes and non-athletes in Finland.MethodsIn this cross-sectional study, a musculoskeletal examination assessing posture, mobility and movement control was carried out by a sports and exercise medicine physician on 399 athletes aged 14–17 years and 177 non-athletes. Within 2 weeks another sports and exercise medicine physician repeated the examination for 41 adolescents to test the inter-rater repeatability.ResultsIn total, 10 of the 11 tests performed had at least moderate inter-rater reliability (κ ≥0.4 or percentage agreement >80%). Athletes more often tha…
Intrinsic Lipschitz Graphs and Vertical β-Numbers in the Heisenberg Group
2016
The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group $\mathbb{H}$. In particular, we aim to demonstrate that new phenomena arise compared to the Euclidean theory, founded by G. David and S. Semmes in the 90's. The theory in $\mathbb{H}$ has an apparent connection to certain nonlinear PDEs, which do not play a role with similar questions in $\mathbb{R}^{3}$. Our main object of study are the intrinsic Lipschitz graphs in $\mathbb{H}$, introduced by B. Franchi, R. Serapioni and F. Serra Cassano in 2006. We claim that these $3$-dimensional sets in $\mathbb{H}$, if any, deserve to be called quantitatively $3$-rectifi…
Equivalence of viscosity and weak solutions for the normalized $p(x)$-Laplacian
2018
We show that viscosity solutions to the normalized $p(x)$-Laplace equation coincide with distributional weak solutions to the strong $p(x)$-Laplace equation when $p$ is Lipschitz and $\inf p>1$. This yields $C^{1,\alpha}$ regularity for the viscosity solutions of the normalized $p(x)$-Laplace equation. As an additional application, we prove a Rad\'o-type removability theorem.
Gradient and Lipschitz Estimates for Tug-of-War Type Games
2021
We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz estimate when boundary values are close to a plane. Such estimates are known to play a key role in the higher regularity theory of partial differential equations. The proofs are based on cancellation and coupling methods as well as an improved version of the cylinder walk argument. peerReviewed
Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities
2018
We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega\subset \mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\Omega\times \Omega$ via couplings.