Search results for "neuma"
showing 10 items of 154 documents
Quasi *-algebras of measurable operators
2009
Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For $p\geq 2$ they are also proved to possess a {\em sufficient} family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra $(\X,\Ao)$ possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.
Sharp Poincaré inequalities in a class of non-convex sets
2018
Let $gamma$ be a smooth, non-closed, simple curve whose image is symmetric with respect to the $y$-axis, and let $D$ be a planar domain consisting of the points on one side of $gamma$, within a suitable distance $delta$ of $gamma$. Denote by $mu_1^{odd}(D)$ the smallest nontrivial Neumann eigenvalue having a corresponding eigenfunction that is odd with respect to the $y$-axis. If $gamma$ satisfies some simple geometric conditions, then $mu_1^{odd}(D)$ can be sharply estimated from below in terms of the length of $gamma$ , its curvature, and $delta$. Moreover, we give explicit conditions on $delta$ that ensure $mu_1^{odd}(D)=mu_1(D)$. Finally, we can extend our bound on $mu_1^{odd}(D)$ to a …
Landesman-Lazer type (p, q)-equations with Neumann condition
2020
We consider a Neumann problem driven by the (p, q)-Laplacian under the Landesman-Lazer type condition. Using the classical saddle point theorem and other classical results of the calculus of variations, we show that the problem has at least one nontrivial weak solution.
Morse-Smale index theorems for elliptic boundary deformation problems.
2012
AbstractMorse-type index theorems for self-adjoint elliptic second order boundary value problems arise as the second variation of an energy functional corresponding to some variational problem. The celebrated Morse index theorem establishes a precise relation between the Morse index of a geodesic (as critical point of the geodesic action functional) and the number of conjugate points along the curve. Generalization of this theorem to linear elliptic boundary value problems appeared since seventies. (See, for instance, Smale (1965) [12], Uhlenbeck (1973) [15] and Simons (1968) [11] among others.) The aim of this paper is to prove a Morse–Smale index theorem for a second order self-adjoint el…
Evolution problems of Leray-Lions type with nonhomogeneous Neumann boundary conditions in metric random walk spaces
2019
Abstract In this paper we study evolution problems of Leray–Lions type with nonhomogeneous Neumann boundary conditions in the framework of metric random walk spaces. This covers cases with the p -Laplacian operator in weighted discrete graphs and nonlocal operators with nonsingular kernel in R N .
Nonexistence of global weak solutions for a nonlinear Schrodinger equation in an exterior domain
2020
We study the large-time behavior of solutions to the nonlinear exterior problem L u ( t , x ) = &kappa
Fractional Laplacians in bounded domains: Killed, reflected, censored, and taboo Lévy flights.
2018
The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data respecting fractional Laplacian should actually be. This ambiguity holds true not only for each specific choice of the process behavior at the boundary (like e.g. absorbtion, reflection, conditioning or boundary taboos), but extends as well to its particular technical implementation (Dirchlet, Neumann, etc. problems). The inferred jump-type …
Rings with algebraic n-engel elements
1994
(1994). Rings with algebraic n-engel elements. Communications in Algebra: Vol. 22, No. 5, pp. 1685-1701.
Possible extensions of the noncommutative integral
2011
In this paper we will discuss the problem of extending a trace σ defined on a dense von Neumann subalgebra \(\mathfrak{M}\) of a topological *-algebra \({\mathfrak{A}}\) to some subspaces of \({\mathfrak{A}}\). In particular, we will prove that extensions of the trace σ that go beyond the space L1(σ) really exist and we will explicitly construct one of these extensions. We will continue the analysis undertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745–1777, 2010) on the general problem of extending positive linear functionals on a *-algebra.
Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems
2013
In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p > 1) in a Lipschitz bounded domain Ω in ℝn. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.