Search results for "Conti"
showing 10 items of 3486 documents
Hölder stability for Serrin’s overdetermined problem
2015
In a bounded domain \(\varOmega \), we consider a positive solution of the problem \(\Delta u+f(u)=0\) in \(\varOmega \), \(u=0\) on \(\partial \varOmega \), where \(f:\mathbb {R}\rightarrow \mathbb {R}\) is a locally Lipschitz continuous function. Under sufficient conditions on \(\varOmega \) (for instance, if \(\varOmega \) is convex), we show that \(\partial \varOmega \) is contained in a spherical annulus of radii \(r_i 0\) and \(\tau \in (0,1]\). Here, \([u_\nu ]_{\partial \varOmega }\) is the Lipschitz seminorm on \(\partial \varOmega \) of the normal derivative of u. This result improves to Holder stability the logarithmic estimate obtained in Aftalion et al. (Adv Differ Equ 4:907–93…
Adaptive rational interpolation for point values
2019
Abstract G. Ramponi et al. introduced in Carrato et al. (1997,1998), Castagno and Ramponi (1996) and Ramponi (1995) a non linear rational interpolator of order two. In this paper we extend this result to get order four. We observe the Gibbs phenomenon that is obtained near discontinuities with its weights. With the weights we propose we obtain approximations of order four in smooth regions and three near discontinuities. We also introduce a rational nonlinear extrapolation which is also of order four in the smooth region of the given function. In the experiments we calculate numerically approximation orders for the different methods described in this paper and see that they coincide with th…
Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions
2014
Abstract Let ( X , d , μ ) be a complete, locally doubling metric measure space that supports a local weak L 2 -Poincare inequality. We show that optimal gradient estimates for Cheeger-harmonic functions imply local isoperimetric inequalities.
Singular integrals on regular curves in the Heisenberg group
2019
Let $\mathbb{H}$ be the first Heisenberg group, and let $k \in C^{\infty}(\mathbb{H} \, \setminus \, \{0\})$ be a kernel which is either odd or horizontally odd, and satisfies $$|\nabla_{\mathbb{H}}^{n}k(p)| \leq C_{n}\|p\|^{-1 - n}, \qquad p \in \mathbb{H} \, \setminus \, \{0\}, \, n \geq 0.$$ The simplest examples include certain Riesz-type kernels first considered by Chousionis and Mattila, and the horizontally odd kernel $k(p) = \nabla_{\mathbb{H}} \log \|p\|$. We prove that convolution with $k$, as above, yields an $L^{2}$-bounded operator on regular curves in $\mathbb{H}$. This extends a theorem of G. David to the Heisenberg group. As a corollary of our main result, we infer that all …
Approximation and quasicontinuity of Besov and Triebel–Lizorkin functions
2016
We show that, for $0<s<1$, $0<p<\infty$, $0<q<\infty$, Haj\l asz-Besov and Haj\l asz-Triebel-Lizorkin functions can be approximated in the norm by discrete median convolutions. This allows us to show that, for these functions, the limit of medians, \[ \lim_{r\to 0}m_u^\gamma(B(x,r))=u^*(x), \] exists quasieverywhere and defines a quasicontinuous representative of $u$. The above limit exists quasieverywhere also for Haj\l asz functions $u\in M^{s,p}$, $0<s\le 1$, $0<p<\infty$, but approximation of $u$ in $M^{s,p}$ by discrete (median) convolutions is not in general possible.
Norm or numerical radius attaining polynomials on C(K)
2004
Abstract Let C(K, C ) be the Banach space of all complex-valued continuous functions on a compact Hausdorff space K. We study when the following statement holds: every norm attaining n-homogeneous complex polynomial on C(K, C ) attains its norm at extreme points. We prove that this property is true whenever K is a compact Hausdorff space of dimension less than or equal to one. In the case of a compact metric space a characterization is obtained. As a consequence we show that, for a scattered compact Hausdorff space K, every continuous n-homogeneous complex polynomial on C(K, C ) can be approximated by norm attaining ones at extreme points and also that the set of all extreme points of the u…
Monotonicity-based inversion of the fractional Schr\"odinger equation II. General potentials and stability
2019
In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness results for the fractional Calder\'on problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Sch…
Orbital chronology of the lower-middle Aptian: palaeoenvironmental implications (Serre Chaitieu section, Vocontian Basin).
2013
4 pages; International audience; A detailed cyclostratigraphic study conducted on several proxies including spectral gamma ray, magnetic susceptibility, clay minerals, and carbonate content suggests that the return to equilibrium in the carbon cycle after the major disturbance linked with Oceanic Anoxic Event 1a occurred in about 2 Myr. The minimum duration of the D. furcata zone is estimated at 0.46 Myr and that of the E. subnodosocostatum zone at 1.45 Myr. Strengthening of the obliquity record in the furcata zone confirms the cooling that characterizes this period.
Modes of motion in a confined colloidal suspension under shear
2004
We investigated aqueous suspensions of charged polystyrene latex spheres at low salt concentration under the combined influence of steady shear and confining walls. Their equilibrium structure was adjusted via the particle and salt concentration to be either fluid or body centred cubic. Using high-resolution real-space microscopy, we here present a first direct observation of collective modes of motion under shear. As a function of either shear rate and/or salt concentration, we find a continuous transition from registered to free sliding of layers accompanied by an equally continuous structural rearrangement lowering the dimensionality of long-ranged order.
Original Supercritical Water Device for Continuous Production of Nanopowders
2011
Well-crystallized ZnO, ZrO2, TiO2, CeO2, Y2O3 and La2O3 nanoparticles are synthesized under supercritical water conditions (T > 647 K and P > 22.1 MPa) using a home-made continuous process. At room temperature, metallic salts with or without aqueous hydroxide solution (KOH or NaOH) are pressurized to 25–30 MPa. Then, the reactant(s) is/are rapidly heated to 673–773 K by mixing with the supercritical water in a patented reactor. Residence time is in the range from 2 to 8 s. XRD, TEM and surface area analyses highlight the production of pure and well-crystallized nanoparticles with a uniform size distribution.