1,721,773 research outputs found
Schwarz P surfaces and a non local perturbation of the perimeter
No full textIn the paper, we consider a small non local perturbation of the perimeter and we construct at least four critical points close to suitable translations of the Schwarz P surface with fixed volume
Clifford Tori and the singularly perturbed Cahn–Hilliard equation
Full text linkIn this paper we construct entire solutions us to the Cahn-Hilliard equation , under the volume constraint , with c(epsilon) -> 1 as epsilon -> 0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio embedded in , as epsilon -> 0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov-Schmidt reduction and on careful geometric expansions of the Laplacian
Radial and cylindrical symmetry of solutions to the Cahn-Hilliard equation
Full text linkThe paper is devoted to the classification of entire solutions to the Cahn–Hilliard equation
−u = u −u3 −δ in RN , with particular interest in those solutions whose nodal set is either
bounded or contained in a cylinder. The aim is to prove either radial or cylindrical symmetry,
under suitable hypothesis.Projekt DEA
k-ended O(m)×O(n) invariant solutions to the Allen-Cahn equation with infinite Morse index
Full text linkIn this work we study existence, asymptotic behaviour and stability properties of O(m) x O(n)-invariant solutions of the Allen-Cahn equation Delta u + u(1 - u(2)) = 0 in R-m x R-n with m, n >= 2 and m + n >= 8. We exhibit four families of solutions whose nodal sets are smooth logarithmic corrections of the Lawson cone and with infinite Morse index. This work complements the study started in [23] by Pacard and Wei and [1] by Agudelo, Kowalczyk and Rizzi
Positive and nodal single-layered solutions to supercritical elliptic problems above the higher critical exponents
Full text linkWe study the problem
−Δv + \lambda v = |v|^{p−2} v in Ω, v = 0 on \partial Ω,
for \lambda\in R and supercritical exponents p, in domains of the form
Ω := {(y, z)\in R^{N−m−1} × R^{m+1} : (y, |z|) \in Θ},
where m \ge 1, N − m \ge 3, and Θ is a bounded domain in RN−m whose
closure is contained in \R^{N−m−1} ×(0,1). Under some symmetry assumptions
on Θ, we show that this problem has infinitely many solutions for every \lambda
in an interval which contains [0,1) and p > 2 up to some number which is
larger than the (m+ 1)st critical exponent 2^*_
{N,m} := \frac{2(N−m)}{N−m−2} . We also exhibit
domains with a shrinking hole, in which there are a positive and a nodal
solution which concentrate on a sphere, developing a single layer that blows
up at an m-dimensional sphere contained in the boundary of Ω, as the hole
shrinks and p \to 2^*_{N,m} from above. The limit profile of the positive solution,
in the transversal direction to the sphere of concentration, is a rescaling of
the standard bubble, whereas that of the nodal solution is a rescaling of a
nonradial sign-changing solution to the problem
−Δu = |u|2^*_{n−2} u, u\in D^{1,2}(\R^n),
where 2^*_n := \frac{2n}{n−2} is the critical exponent in dimension n
Normalized solutions of mass supercritical Schrödinger–Poisson equation with potential
Full text linkIn this paper we prove the existence of normalized solutions (lambda, u), subset of (0, infinity) x H-1(R-3) to the following Schrodinger-Poisson equation { -Delta u + V(x)u + )u + (|x|(-1) * u(2))u = |u|(p-2)u in R-3, u > 0, integral(3)(R) u(2)dx = a(2), where a > 0 is fixed, p is an element of ( 10/3 , 6) is a given exponent and the potential V satisfies some suitable conditions. Since the L-2(R-3)-norm of u is fixed, ) appears as a Lagrange multiplier. For V (x) >= 0, our solutions are obtained by using a mountain-pass argument on bounded domains and a limit process introduced by Bartsch et al (Commun Partial Differ Equ 46:1729-1756, 2021). For V (x) <= 0, we directly construct an entire mountain-pass solution with positive energy
The Jacobi operator of some special minimal hypersurfaces
Full text linkIn this work we discuss stability and nondegeneracy properties of some special families of minimal hypersurfaces embedded in RmxRn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\mathbb {R}<^>m\times \mathbb {R}<^>n\end{document} with m,n >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. These hypersurfaces are asymptotic at infinity to a fixed Lawson cone Cm,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. In the case m+n >= 8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, we show that such hypersurfaces are strictly stable and we provide a full classification of their bounded Jacobi fields, which in turn allows us to prove the non-degeneracy of such surfaces. In the case m+n <= 7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, we prove that such hypersurfaces have infinite Morse index
Evaluation of Technology Options for Substrate noise reduction
No full textSubstrate coupling is a phenomenon that affects the behavior and performance of RF and mixed signal ICs. Prediction of such crosstalk during the design process can help designers. In this paper, a new methodology is presented for performing a fast and reliable characterization of the noise transmission path, modeling the substrate as a resistive network. Adopting only DC measurement techniques, the dependence of disturbances attenuation on the geometric parameters is found. Moreover, the relation between attenuation and disturbance types is indicated. Finally, a qualitative comparison is made between the efficiency of the most commonly used technology measures against substrate crosstalk
High-speed error correction circuit based on iterative cells
No full textThe implementation of a decoder for cyclic redundancy check codes at very high bit rates is suggested. it is based on a purely combinational, iterative cells circuit. The theoretical performance evaluation and the simulations show the enhancement in terms of operating speed with respect to the sequential solution
Multiple Delaunay ends solutions of the Cahn-Hilliard equation
Full text linkLet Sigma be a surface of constant mean curvature in R-3 with multiple Delaunay ends. Assuming that Sigma is non degenerate in this paper we construct new solutions to the Cahn-Hilliard equation epsilon Delta u + epsilon(-1)u(1 - u(2)) = l(epsilon) in R-3 such that as epsilon -> 0 the zero level set of u(epsilon) approaches Sigma. Moreover, on compacts of the connected components of R-3\Sigma we have 1 - vertical bar u(epsilon)vertical bar -> 0 uniformly
- …
