Search results for "Bounded"
showing 10 items of 658 documents
A Density Result for Homogeneous Sobolev Spaces on Planar Domains
2018
We show that in a bounded simply connected planar domain $\Omega$ the smooth Sobolev functions $W^{k,\infty}(\Omega)\cap C^\infty(\Omega)$ are dense in the homogeneous Sobolev spaces $L^{k,p}(\Omega)$.
Nonlinear scalar field equations with general nonlinearity
2018
Consider the nonlinear scalar field equation \begin{equation} \label{a1} -\Delta{u}= f(u)\quad\text{in}~\mathbb{R}^N,\qquad u\in H^1(\mathbb{R}^N), \end{equation} where $N\geq3$ and $f$ satisfies the general Berestycki-Lions conditions. We are interested in the existence of positive ground states, of nonradial solutions and in the multiplicity of radial and nonradial solutions. Very recently Mederski [30] made a major advance in that direction through the development, in an abstract setting, of a new critical point theory for constrained functionals. In this paper we propose an alternative, more elementary approach, which permits to recover Mederski's results on the scalar field equation. T…
Holomorphic mappings of bounded type
1992
Abstract For a Banach space E, we prove that the Frechet space H b(E) is the strong dual of an (LB)-space, B b(E), which leads to a linearization of the holomorphic mappings of bounded type. It is also shown that the holomorphic functions defined on (DFC)-spaces are of uniformly bounded type.
Orlicz-Hardy inequalities
2004
We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary and sufficient, thus extending results of Ancona, Lewis, and Wannebo. peerReviewed
Unbounded C$^*$-seminorms and $*$-Representations of Partial *-Algebras
2009
The main purpose of this paper is to construct *-representations from unbounded C*-seminorms on partial *-algebras and to investigate their *-representations. © Heldermann Verlag.
A density result on Orlicz-Sobolev spaces in the plane
2018
We show the density of smooth Sobolev functions $W^{k,\infty}(\Omega)\cap C^\infty(\Omega)$ in the Orlicz-Sobolev spaces $L^{k,\Psi}(\Omega)$ for bounded simply connected planar domains $\Omega$ and doubling Young functions $\Psi$.
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…
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.
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 ) .
Doubly nonlinear periodic problems with unbounded operators
2004
Abstract The solvability of the evolution system v ′( t )+ B ( t ) u ( t )∋ f ( t ), v ( t )∈ A ( t ) u ( t ), 0 t T , with the periodic condition v (0)= v ( T ) is investigated in the case where A (t) are bounded, possibly degenerate, subdifferentials and B (t) are unbounded subdifferentials.