Search results for "Mathematical analysis"

L∞-variational problem associated to dirichlet forms

2012

A note on monolithic scattered compacta

2015

Abstract For a Banach space E, it is well-known that a necessary condition for E to have the controlled separable complementation property (CSCP, for short) is that the dual unit ball B E ⁎ be monolithic in the weak-star topology. We prove here that when X is a scattered first countable locally compact space, then monolithicity of X turns out to be sufficient for C 0 ( X ) to enjoy the CSCP.

Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space

2015

We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of R n and the relation between these spaces and traces of classical Sobolev spaces. This extends in a certain way the results of Shvartsman (20) to the case of lower dimensional subsets of the Euclidean space.

OBSTACLE PROBLEMS FOR DEGENERATE ELLIPTIC EQUATIONS WITH NONHOMOGENEOUS NONLINEAR BOUNDARY CONDITIONS

2008

In this paper we study the questions of existence and uniqueness of solutions for equations of type - div a(x,Du) + γ(u) ∋ ϕ, posed in an open bounded subset Ω of ℝN, with nonlinear boundary conditions of the form a(x,Du) · η + β(u) ∋ ψ. The nonlinear elliptic operator div a(x,Du) modeled on the p-Laplacian operator Δp(u) = div (|Du|p-2Du), with p > 1, γ and β maximal monotone graphs in ℝ2 such that 0 ∈ γ(0) ∩ β(0), [Formula: see text] and the data ϕ ∈ L1(Ω) and ψ ∈ L1(∂ Ω). Since D(γ) ≠ ℝ, we are dealing with obstacle problems. For this kind of problems the existence of weak solution, in the usual sense, fails to be true for nonhomogeneous boundary conditions, so a new concept of solut…

Iterative construction of Dupin cyclides characteristic circles using non-stationary Iterated Function Systems (IFS)

2012

International audience; A Dupin cyclide can be defined, in two different ways, as the envelope of an one-parameter family of oriented spheres. Each family of spheres can be seen as a conic in the space of spheres. In this paper, we propose an algorithm to compute a characteristic circle of a Dupin cyclide from a point and the tangent at this point in the space of spheres. Then, we propose iterative algorithms (in the space of spheres) to compute (in 3D space) some characteristic circles of a Dupin cyclide which blends two particular canal surfaces. As a singular point of a Dupin cyclide is a point at infinity in the space of spheres, we use the massic points defined by J.C. Fiorot. As we su…

FREDHOLM THEORY FOR DEGENERATE PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH FIBERED BOUNDARIES

2001

We consider the calculus Ψ*,* de(X, deΩ½) of double-edge pseudodifferential operators naturally associated to a compact manifold X whose boundary is the total space of a fibration. This fits into the setting of boundary fibration structures, and we discuss the corresponding geometric objects. We construct a scale of weighted double-edge Sobolev spaces on which double-edge pseudodifferential operators act as bounded operators, characterize the Fredholm elements in Ψ*,* de(X) by means of the invertibility of an appropriate symbol map, and describe a K-theoretical formula for the Fredholm index extending the Atiyah–Singer formula for closed manifolds. The algebra of operators of order (0, 0) i…

Spaces of holomorphic functions in regular domains

2009

AbstractLet Ω be a regular domain in the complex plane C, Ω≠C. Let Gb(Ω) be the linear space over C of the holomorphic functions f in Ω such that f(n) is bounded in Ω and is continuously extendible to the closure Ω¯ of Ω, n=0,1,2,… . We endow Gb(Ω), in a natural manner, with a structure of Fréchet space and we obtain dense subspaces F of Gb(Ω), with good topological linear properties, also satisfying that each function f of F, distinct from zero, does not extend holomorphically outside Ω.

A new proof of the support theorem and the range characterization for the Radon transform

1983

The aim of this note is to give a new and elementary proof of the support theorem for the Radon transform, which is based only on the projection theorem and the Paley-Wiener theorem for the Fourier transform. The idea is to solve a certain system of linear equations in order to determine the coefficients of a homogeneous polynomial (interpolation problem). By the same method, we get a short proof of the range characterization for Radon transforms of functions supported in a ball.

Fenchel type theorems for submanifolds of S n

1996

Common fixed points in cone metric spaces

2007

In this paper we consider a notion of g-weak contractive mappings in the setting of cone metric spaces and we give results of common fixed points. This results generalize some common fixed points results in metric spaces and some of the results of Huang and Zhang in cone metric spaces.