Big pieces of -graphs for minimizers of the Mumford-Shah functional
Séverine Rigot (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Bradley, Mary Elizabeth, Lenhart, Suzanne (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
K. Zhang (1990)
Annales de l'I.H.P. Analyse non linéaire
Sista Sivaji Ganesh, Muthusamy Vanninathan (2005)
ESAIM: Control, Optimisation and Calculus of Variations
In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a regular Bloch spectrum is not guaranteed. The aim here is to develop all necessary spectral tools to overcome...
Sista Sivaji Ganesh, Muthusamy Vanninathan (2010)
ESAIM: Control, Optimisation and Calculus of Variations
In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a regular Bloch spectrum is not guaranteed. The aim here is to develop all necessary spectral tools to overcome...
Gian Paolo Leonardi (2000)
Rendiconti del Seminario Matematico della Università di Padova
Valentino Magnani (2006)
Open Mathematics
We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence...
Fiorenza, Alberto (1997)
Journal of Convex Analysis
Kobra Rabiei, Yadollah Ordokhani (2018)
Applications of Mathematics
A new hybrid of block-pulse functions and Boubaker polynomials is constructed to solve the inequality constrained fractional optimal control problems (FOCPs) with quadratic performance index and fractional variational problems (FVPs). First, the general formulation of the Riemann-Liouville integral operator for Boubaker hybrid function is presented for the first time. Then it is applied to reduce the problems to optimization problems, which can be solved by the existing method. In this way we find...
Giuseppe Cardone, Sergei A. Nazarov, Keijo Ruotsalainen (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 − ε, where ε > 0 is a small real parameter, i.e. the waveguide is gently converging. The width of the junction zone for the semi-strips is 1 + O(√ε). We will present a sufficient condition for the existence of a weakly coupled bound state below π2, the lower bound of the continuous spectrum. This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when ε → 0+....
Italo Tamanini (1982)
Journal für die reine und angewandte Mathematik
Eduardo H. A. Gonzales, Umberto Massari, Italo Tamanini (1993)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
The existence of a singular curve in is proven, whose curvature can be extended to an function. The curve is the boundary of a two dimensional set, minimizing the length plus the integral over the set of the extension of the curvature. The existence of such a curve was conjectured by E. De Giorgi, during a conference held in Trento in July 1992.
Robert Gulliver, S. Hildebrandt (1986)
Manuscripta mathematica
Toni Lassila, Andrea Manzoni, Alfio Quarteroni, Gianluigi Rozza (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded, for which the worst-case in terms of recirculation effects is inferred to correspond to a strong orifice flow through near-complete occlusion.A worst-case optimal control approach is applied to the steady Navier-Stokes...
Póvoas, M. (1982)
Portugaliae mathematica
El-Saify, Hussain A. (2001)
International Journal of Mathematics and Mathematical Sciences
Daniela Giachetti, Rosanna Schianchi (1997)
Studia Mathematica
Karsten Eppler (2000)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
For a shape optimization problem second derivatives are investigated, obtained by a special approach for the description of the boundary variation and the use of a potential ansatz for the state. The natural embedding of the problem in a Banach space allows the application of a standard differential calculus in order to get second derivatives by a straight forward "repetition of differentiation". Moreover, by using boundary value characerizations for more regular data, a complete boundary integral...
Dorin Bucur, Jean-Paul Zolésio (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
J. Jost, M. Meier (1983)
Mathematische Annalen