Search results for "HT"
showing 10 items of 20594 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 .
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, infp>1, and f is continuous and bounded. 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.
The ALICE experiment at the CERN LHC
2008
Journal of Instrumentation 3(08), S08002 (2008). doi:10.1088/1748-0221/3/08/S08002
Vista e visione dell'architetto
2015
Il paper affronta il tema del'atto del vedere dell'architetto in chiave fenomenolgica ma anche affrontando l'intreccio tra cecità e vista a partire dalle riflessioni di Derrida. Il concetto di Design Thinking viene proposto, con riferimento al noto Visual Thinking di Rudolf Arnheim. Si può ipotizzare un modo di vedere specifico degli architetti nel quale immaginazione e visione di fondono e sovrappongono a partire dalla memoria. Lo schematismo di Kant, ripreso con riferimento all'arte e all'architettura, da Cesare Brandi costituisce la teoria-chiave per la quale visione e immaginazione possono essere concepite come risvolti del medesimo concetto. La cecità, intesa come luogo altro della vis…
Visuaalinen tutkimus elämys- ja seikkailukokemusten merkityksistä opiskelijoille luontoliikuntakurssilla Norjassa
2014
Linjama, Leena. 2014. Visuaalinen tutkimus elämys- ja seikkailukokemusten merkityksistä opiskelijoille luontoliikuntakurssilla Norjassa. Liikuntakasvatuksen laitos, Jyväskylän yliopis-to. Liikuntapedagogiikan pro gradu –tutkielma, 66s. Tutkimuksen tarkoituksena oli tulkita ja analysoida Oslon liikuntakorkeakouluopiskelijoiden vuoristovaellukselta saamia henkilökohtaisesti merkityksellisiä hetkiä heidän itse ottamien valokuvien ja lyhyiden kirjallisten kuvausten avulla. Tämä 7 päivän vuoristovaellus Jotun-heimenin vuoristossa kuului 30 opintopisteen outdoor studies –opinto-kokonaisuuteen, jota pääsin opiskelemaan opiskelijavaihdon aikana syksyllä 2013 Oslossa. Osallistuin itse koko-naisvalta…
Anatomic and functional follow-up of patients with an idiopathic epiretinal membrane and a preserved visual acuity
2013
Purpose: To determine the anatomic and functional retinal modifications in patients with an idiopathic epiretinal membrane (ERM) and a preserved visual acuity (VA).Methods: Monocentric, prospective study in 24 eyes of 24 patients with an ERM and a VA better than 20/25. Recorded data were best corrected VA on ETDRS scale, retinal anatomic lesions on spectral-domain OCT, retinal sensitivities on microperimetry and macular and foveal thicknesses at 0 and 6 months.Results: At inclusion, mean VA was 84 ± 5 letters, mean macular sensitivity was 14.0 ± 1.4 decibels (dB) and mean foveal sensitivity was 14,4 ± 1,5 dB. Mean macular thickness was 351 ± 34 µm and mean foveal thickness was 348 ± 66 µm. …
Motion perception in early glaucoma
2013
Purpose: The aim of our study was to underline the changes in the movement perception for early glaucoma. Our working hypothesis consisted in inquiring if the impairment of the magnocellular pathway may modify the movement perception capabilities in the visual field, more particularly in its peripheral area.Methods: We included 14 healthy subjects and 14 patients with early primary open angle glaucoma. A moving target was presented on a semicircular screen (1.8 m diameter); participants were asked to localize the Ending Point (EP) of each movement. Each stimulus consisted in a white dot (0,72° of diameter) moving horizontally with the imposed velocity profile. Two different laws of motion w…
Researching Children’s Multiple Family Relations: Social Network Maps and Life-Lines as Methods
2015
Visual methods are reported to have certain advantages when conducting interviews on sensitive topics, such as intimate spaces, home-related ethical issues, and vulnerable families. In this article, we concentrate on two visual methods: social network maps and life-lines. In our research project on children’s well-being and emotional security in multiple family relations, we collected data by interviewing children and asking them to complete social network maps and life-lines. We discuss the suitability of these two visual methods for describing children’s close relationships with their family members and significant others. Combining these two methods during an interview process with child…