Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of genus two Riemann surfaces
2005
We study extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of compact genus two Riemann surfaces. By a combination of analytical and numerical methods we identify four non-degenerate critical points of this function and compute the signature of the Hessian at these points. The curve with the maximal number of automorphisms (the Burnside curve) turns out to be the point of the absolute maximum. Our results agree with the mass formula for orbifold Euler characteristics of the moduli space. A similar analysis is performed for the Bolza's strata of symmetric Riemann surfaces of genus two.
Heat semi-group and generalized flows on complete Riemannian manifolds
2011
Abstract We will use the heat semi-group to regularize functions and vector fields on Riemannian manifolds in order to develop Di Perna–Lions theory in this setting. Malliavinʼs point of view of the bundle of orthonormal frames on Brownian motions will play a fundamental role. As a byproduct we will construct diffusion processes associated to an elliptic operator with singular drift.
Homogenization of the wave equation in composites with imperfect interface : a memory effect
2007
Abstract In this paper we study the asymptotic behaviour of the wave equation with rapidly oscillating coefficients in a two-component composite with e-periodic imperfect inclusions. We prescribe on the interface between the two components a jump of the solution proportional to the conormal derivatives through a function of order e γ . For the different values of γ, we obtain different limit problems. In particular, for γ = 1 we have a linear memory effect in the homogenized problem.
Regularity of solutions to differential equations with non-Lipschitz coefficients
2008
AbstractWe study the ordinary and stochastic differential equations whose coefficients satisfy certain non-Lipschitz conditions, namely, we study the behaviors of small subsets under the flows generated by these equations.
Bohr radii of vector valued holomorphic functions
2012
Abstract Motivated by the scalar case we study Bohr radii of the N -dimensional polydisc D N for holomorphic functions defined on D N with values in Banach spaces.
Annihilating sets for the short time Fourier transform
2010
Abstract We obtain a class of subsets of R 2 d such that the support of the short time Fourier transform (STFT) of a signal f ∈ L 2 ( R d ) with respect to a window g ∈ L 2 ( R d ) cannot belong to this class unless f or g is identically zero. Moreover we prove that the L 2 -norm of the STFT is essentially concentrated in the complement of such a set. A generalization to other Hilbert spaces of functions or distributions is also provided. To this aim we obtain some results on compactness of localization operators acting on weighted modulation Hilbert spaces.
Generalized evolutes, vertices and conformal invariants of curves in Rn + 1
1999
Abstract We define the generalized evolute of a curve in ( n + 1)-space and find a duality relation between them. We also prove that the conformal torsion is a function of the speed of the generalized evolute and that the singular points of the generalized evolute (vertices) are conformal invariants.
Menger curvature and rectifiability in metric spaces
2008
We show that for any metric space $X$ the condition \[ \int_X\int_X\int_X c(z_1,z_2,z_3)^2\, d\Hm z_1\, d\Hm z_2\, d\Hm z_3 < \infty, \] where $c(z_1,z_2,z_3)$ is the Menger curvature of the triple $(z_1,z_2,z_3)$, guarantees that $X$ is rectifiable.
Conformal curvatures of curves in
2001
Abstract We define a complete set of conformal invariants for pairs of spheres in and obtain from these the expressions of the conformal curvatures of curves in (n + 1)-space in terms of the Euclidean invariants.
Superlinear (p(z), q(z))-equations
2017
AbstractWe consider Dirichlet boundary value problems for equations involving the (p(z), q(z))-Laplacian operator in the principal part and prove the existence of one and three nontrivial weak solutions, respectively. Here, the nonlinearity in the reaction term is allowed to depend on the solution, but does not satisfy the Ambrosetti–Rabinowitz condition. The hypotheses on the reaction term ensure that the Euler–Lagrange functional, associated to the problem, satisfies both the -condition and a mountain pass geometry.