The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform

Alessandro Giacomini - One of the best experts on this subject based on the ideXlab platform.

  • Best constant in Poincaré inequalities with traces: A free discontinuity approach
    Annales de l'Institut Henri Poincaré C Analyse non linéaire, 2019
    Co-Authors: Dorin Bucur, Alessandro Giacomini, Paola Trebeschi
    Abstract:

    Abstract For Ω ⊂ R N open bounded and with a Lipschitz boundary, and 1 ≤ p + ∞ , we consider the Poincare inequality with trace term C p ( Ω ) ‖ u ‖ L p ( Ω ) ≤ ‖ ∇ u ‖ L p ( Ω ; R N ) + ‖ u ‖ L p ( ∂ Ω ) on the Sobolev space W 1 , p ( Ω ) . We show that among all domains Ω with Prescribed Volume, the constant is minimal on balls. The proof is based on the analysis of a free discontinuity problem.

  • Optimal Shapes Maximizing the Steklov Eigenvalues
    SIAM Journal on Mathematical Analysis, 2017
    Co-Authors: Beniamin Bogosel, Doina Bucur, Alessandro Giacomini
    Abstract:

    In this paper we consider the problem of maximizing the $k$th Steklov eigenvalue of the Laplacian (or a more general spectral functional), among all sets of ${\mathbb R}^d$ of Prescribed Volume. We prove existence of an optimal set and get some qualitative properties of the solutions in a relaxed setting. In particular, in ${\mathbb R}^2$, we prove that the optimal set consists in the union of at most $k$ disjoint Jordan domains with finite perimeter. A key point of our analysis is played by an isodiametric control of the Stelkov spectrum. We also perform some numerical experiments and exhibit the optimal shapes maximizing the $k$th eigenvalues under area constraint in ${\mathbb R}^2$ for $k=1, \dots,10$.

  • a variational approach to the isoperimetric inequality for the robin eigenvalue problem
    Archive for Rational Mechanics and Analysis, 2010
    Co-Authors: Dorin Bucur, Alessandro Giacomini
    Abstract:

    The isoperimetric inequality for the first eigenvalue of the Laplace operator with Robin boundary conditions was recently proved by Daners in the context of Lipschitz sets. This paper introduces a new approach to the isoperimetric inequality, based on the theory of special functions of bounded variation (SBV). We extend the notion of the first eigenvalue λ1 for general domains with finite Volume (possibly unbounded and with irregular boundary), and we prove that the balls are the unique minimizers of λ1 among domains with Prescribed Volume.

Xiaoqiang Wang - One of the best experts on this subject based on the ideXlab platform.

  • modelling and simulations of multi component lipid membranes and open membranes via diffuse interface approaches
    Journal of Mathematical Biology, 2007
    Co-Authors: Xiaoqiang Wang
    Abstract:

    Diffuse interface (phase field) models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic bending energy and the line tension energy with Prescribed Volume and surface area constraints. By comparing our numerical simulations with recent biological experiments, it is demonstrated that the diffuse interface models can effectively capture the rich phenomena associated with the multi-component vesicle transformation and thus offering great functionality in their simulation and modelling.

  • Modelling and Simulations of Multi-component Lipid Membranes and Open Membranes via Diffusive Interface Approaches
    arXiv: Biological Physics, 2006
    Co-Authors: Xiaoqiang Wang
    Abstract:

    In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic bending energy and the line tension energy with Prescribed Volume and surface area constraints. By comparing our numerical simulations with recent experiments, it is demonstrated that the phase field models can capture the rich phenomena associated with the membrane transformation, thus it offers great functionality in the simulation and modeling of multicomponent membranes.

  • a phase field approach in the numerical study of the elastic bending energy for vesicle membranes
    Journal of Computational Physics, 2004
    Co-Authors: Qiang Du, Xiaoqiang Wang
    Abstract:

    In this paper, we compute the equilibrium configurations of a vesicle membrane under elastic bending energy, with Prescribed Volume and surface area. A variational phase field method is developed for such a problem. Discrete finite difference approximations and numerical simulations are carried out in the axial symmetrical cases. Different energetic bifurcation phenomena are discussed.

Mifodijus Sapagovas - One of the best experts on this subject based on the ideXlab platform.

  • Solution of the system of parametric equations of the sessile drop
    Mathematical Modelling and Analysis, 2002
    Co-Authors: Regimantas Čiupaila, Mifodijus Sapagovas
    Abstract:

    Abstract Several models of parameterization for the problem of free surface of the sessile liquid drop with nonlocal integral condition of Prescribed Volume are considered. The paper aims to obtain for every model specific algebraic connection among physical and geometrical parameters of the problem and compare them. This connection allows to construct the iterative process for the unknown radius of the drop with more simple boundary conditions. The positiveness of Lagrange multiplier in the problem of constrained minimization as well as uniqueness of positive meaning of the radius of the drop are proven in the paper.

Ben Weinkove - One of the best experts on this subject based on the ideXlab platform.

  • Gauduchon metrics with Prescribed Volume form
    Acta Mathematica, 2017
    Co-Authors: Gábor Székelyhidi, Valentino Tosatti, Ben Weinkove
    Abstract:

    We prove that on any compact complex manifold one can find Gauduchon metrics with Prescribed Volume form. This is equivalent to prescribing the Chern-Ricci curvature of the metrics, and thus solves a conjecture of Gauduchon from 1984.

  • The Calabi-Yau equation on almost-Kahler four-manifolds
    arXiv: Differential Geometry, 2006
    Co-Authors: Ben Weinkove
    Abstract:

    Let (M, \omega) be a compact symplectic 4-manifold with a compatible almost complex structure J. The problem of finding a J-compatible symplectic form with Prescribed Volume form is an almost-K\"ahler analogue of Yau's theorem and is connected to a programme in symplectic topology proposed by Donaldson. We call the corresponding equation for the symplectic form the Calabi-Yau equation. Solutions are unique in their cohomology class. It is shown in this paper that a solution to this equation exists if the Nijenhuis tensor is small in a certain sense. Without this assumption, it is shown that the problem of existence can be reduced to obtaining a C^0 bound on a scalar potential function.

Frank Morgan - One of the best experts on this subject based on the ideXlab platform.