Correction to the paper: local regularity for the solutions of the p-Laplacian on the Heisenberg group. The case
Correctors and field fluctuations for the pϵ(x)-laplacian with rough exponents : The sublinear growth case
A corrector theory for the strong approximation of gradient fields inside periodic composites made from two materials with different power law behavior is provided. Each material component has a distinctly different exponent appearing in the constitutive law relating gradient to flux. The correctors are used to develop bounds on the local singularity strength for gradient fields inside micro-structured media. The bounds are multi-scale in nature and can be used to measure the amplification of applied...
Corrigenda to "Unique continuation for Schrödinger operators" and a remark on interpolation of Morrey spaces.
The purpose of this note is twofold. First it is a corrigenda of our paper [RV1]. And secondly we make some remarks concerning the interpolation properties of Morrey spaces.
Costruzione di spike-layers multidimensionali
Si studiano soluzioni positive dellequazione in , dove , ed è un piccolo parametro positivo. Si impongono in genere condizioni al bordo di Neumann. Quando tende a zero, dimostriamo esistenza di soluzioni che si concentrano su curve o varietà.
Counterexample to the convexity of level sets of solutions to the mean curvature equation
The convexity of level sets of solutions to the mean curvature equation is a long standing open problem. In this paper we give a counterexample to it.
Counterexample to the regularity of weak solution of elliptic systems
Counter-Examples to Boundary Estimates for Two-Dimensional Elliptic Systems.
Counterexamples to Some Conjectures on the Number of Solutions on Nonlinear Equations.
Couplage entre éléments finis et calculs analytiques pour l'équation de Laplace dans un domaine à frontière angulaire
Covariant differential operators and Green's functions
The basic idea of this paper is to use the covariance of a partial differential operator under a suitable group action to determine suitable associated Green’s functions. For instance, we offer a new proof of a formula for Green’s function of the mth power of the ordinary Laplace’s operator Δ in the unit disk found in a recent paper (Hayman-Korenblum, J. Anal. Math. 60 (1993), 113-133). We also study Green’s functions associated with mth powers of the Poincaré invariant Laplace operator . It turns...
Crack detection by the topological gradient method
Crack detection using electrostatic measurements
In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical implementation...
Crack detection using electrostatic measurements
In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical...
Critère d'existence de solutions positives pour des équations semi-linéaires non monotones
Criteria for hypoellipticity
Criteria for ultracontractivity
Critical boundary constants and Pohozaev identity
Critical exponent and minimization problem in
Critical groups computations on a class of Sobolev Banach spaces via Morse index
Critical Neumann problem for nonlinear elliptic systems in exterior domains.