Search results for "Mathematical analysis"

Weighted Hardy inequalities beyond Lipschitz domains

2014

It is a well-known fact that in a Lipschitz domain \Omega\subset R^n a p-Hardy inequality, with weight d(x,\partial\Omega)^\beta, holds for all u\in C_0^\infty(\Omega) whenever \beta<p-1. We show that actually the same is true under the sole assumption that the boundary of the domain satisfies a uniform density condition with the exponent \lambda=n-1. Corresponding results also hold for smaller exponents, and, in fact, our methods work in general metric spaces satisfying standard structural assumptions.

Hypersurfaces of prescribed mean curvature over obstacles

1973

Let ~2 be a bounded domain in the euclidean space IR", n-> 2, with Lipschitz boundary ~ . We shall consider surfaces which are graphs of functions u defined on f2 having prescribed mean curvature H=H(x, u) with the side condition that they should be bounded from below by an obstacle ~b. The case H = 0 (minimal surfaces) has been discussed in detail by several authors, compare [6, 7, 12, 13, 17, 18, 20, 21, 24] of the references. Tomi [-31] has also investigated parametric surfaces with variable H. More general variational problems with obstructions have been discussed in [-9] and [-10]. During the session on "Variationsrechnung", held from June 18th to June 24th, 1972 in Oberwolfach, Mirand…

Stability of switched systems: The single input case

2001

We study the stability of the origin for the dynamical system x(t) = u(t)Ax(t) + (1 − u(t))Bx(t), where A and B are two 2×2 real matrices with eigenvalues having strictly negative real part, x ∊ R2 and u(.) : [0, ∞[→ [0,1] is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). This bidimensional problem assumes particular interest since linear systems of higher dimensions can be reduced to our situation.

Splitting Magnitude Response into Real and Imaginary Parts

2017

The determination of real and imaginary parts from magnitude responses is studied for causal linear time-invariant systems having monotonic impulse responses. It is demonstrated that the problem can be interpreted as a special filtering task in the Mellin transform domain having a diffuse magnitude response bounded by the magnitude responses of the filters corresponding to zero and maximum imaginary parts prescribed by the Kronig-Kramers relations. Discrete-time filters processing geometrically sampled magnitude responses are designed for determining the real and imaginary parts. Testing results are presented verifying the performance of the filters.

Bilateral denseness of the hyperbolic limit points of groups acting on metric spaces

1997

Corrigendum to “The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense” [Adv. Math. 272 (2015) 699–742]

2015

Existence and uniqueness for a degenerate parabolic equation with 𝐿¹-data

1999

In this paper we study existence and uniqueness of solutions for the boundary-value problem, with initial datum in L 1 ( Ω ) L^{1}(\Omega ) , u t = d i v a ( x , D u ) in  ( 0 , ∞ ) × Ω , \begin{equation*}u_{t} = \mathrm {div} \mathbf {a} (x,Du) \quad \text {in } (0, \infty ) \times \Omega , \end{equation*} − ∂ u ∂ η a ∈ β ( u ) on  ( 0 , ∞ ) × ∂ Ω , \begin{equation*}-{\frac {{\partial u} }{{\partial \eta _{a}}}} \in \beta (u) \quad \text {on } (0, \infty ) \times \partial \Omega ,\end{equation*} u ( x , 0 ) = u 0 ( x ) in  Ω , \begin{equation*}u(x, 0) = u_{0}(x) \quad \text {in }\Omega ,\end{equation*} where a is a Carathéodory function satisfying the classical Leray-Lions hypothesis, ∂ / …

The asymptotic behavior of the solutions of the Cauchy problem generated by ϕ-accretive operators

2005

Abstract The purpose of this paper is to study the asymptotic behavior of the solutions of certain type of differential inclusions posed in Banach spaces. In particular, we obtain the abstract result on the asymptotic behavior of the solution of the boundary value problem { u t − Δ p ( u ) + | u | γ − 1 u = f on  ] 0 , ∞ [ × Ω , − ∂ u ∂ η ∈ β ( u ) on  [ 0 , ∞ [ × ∂ Ω , u ( 0 , x ) = u 0 ( x ) in  Ω , where Ω is a bounded open domain in R n with smooth boundary ∂Ω, f ( t , x ) is a given L 1 -function on ] 0 , ∞ [ × Ω , γ ⩾ 1 and 1 ⩽ p ∞ . Δ p represents the p-Laplacian operator, ∂ ∂ η is the associated Neumann boundary operator and β a maximal monotone graph in R × R with 0 ∈ β ( 0 ) .

Some Inclusion Theorems for Orlicz and Musielak-Orlicz Type Spaces

1995

where K is a homogeneous kernel and f belongs to some KSthe functional space. In these papers the estimates are taken with respect to the KSthe norm of the space. Recently in [2] we obtained analogous estimates for functions belonging to Orlicz or Musielak-Orlicz type spaces L ~, with respect to the canonical modular functional. These results enable us to say that, for example,

More compact invariant manifolds appearing in the non-linear coupling of oscillators

2006

Abstract Near partially elliptic rest points of generic families of vector fields or transformations, many types of normally hyperbolic invariant compact manifolds can appear, diffeomorphic to intersections of quadrics. To cite this article: M. Chaperon et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).