Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

A finite class of orthogonal functions generated by Routh-Romanovski polynomials

It is known that some orthogonal systems are mapped onto other orthogonal systems by the Fourier transform. In this article we introduce a finite class of orthogonal functions, which is the Fourier transform of Routh-Romanovski orthogonal polynomials, and obtain its orthogonality relation using Parseval identity.

Sharp Sobolev inequality involving a critical nonlinearity on a boundary

We consider the solvability of the Neumann problem for the equation -Delta u + lambda u = 0, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(q-2)u on partial derivative Omega, where Q is a positive and continuous coefficient on partial derivative Omega, lambda is a parameter and q = 2(N - 1)/(N - 2) is a critical Sobolev exponent for the trace embedding of H-1(Omega) into L-q(partial derivative Omega). We investigate the joint effect of the mean curvature of partial derivative Omega and the shape of the graph of Q on the existence of solutions. As a by product we establish a sharp Sobolev inequality for the trace embedding. In Section 6 we establish the existence of solutions when a parameter lambda interferes with the spectrum of -Delta with the Neumann boundary conditions. We apply a min-max principle based on the topological linking.

On a Variational Approach to some Quasilinear Problems

We prove some multiplicity results concerning quasilinear elliptic equations with natural growth conditions. Techniques of nonsmooth critical point theory are employed.

Extended Maximum Principles

2000 Mathematics Subject Classification: 35B50, 35L15.

Analytical and Experimental Investigation of an Ammonia/Air Opposed Reacting Jet

The point-by-point properties of an ammonia/air opposed-reacting-jet flowfield are described by solving the governing partial differential elliptic equations. Analytical descriptions of the reacting flowfield are compared to experimentally measured profiles of temperature and composition. Calculated distributions of stream function, temperature and fuel mole fraction are also presented. © 1972, Taylor & Francis Group, LLC. All rights reserved.

On a Degenerate Parabolic Problem in Holder Spaces

In this paper, we study some degenerate parabolic equation with Cauchy-Dirichlet boundary conditions. This problem is considered in little Holder spaces. The optimal regularity of the solution v is obtained and is specified in terms of those of the second member when some conditions upon the Holder exponent with respect to the degeneracy are satisfied. The proofs mainly use the sum theory of linear operators with or without density of domains and the results of smoothness obtained in the study of some abstract linear differential equations of elliptic type.

Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Sensitivity analysis of a parabolic-elliptic problem

We consider the heat flux through a domain with subregions in which the thermal capacity approaches zero. In these subregions the parabolic heat equation degenerates to an elliptic one. We show the well-posedness of such parabolic-elliptic differential equations for general non-negative L-infinity-capacities and study the continuity of the solutions with respect to the capacity, thus giving a rigorous justification for modeling a small thermal capacity by setting it to zero. We also characterize weak directional derivatives of the temperature with respect to capacity as solutions of related parabolic-elliptic problems.

Applications of elliptic functions to solve differential equations

In questa tesi si mostrano alcune applicazioni degli integrali ellittici nella meccanica Hamiltoniana, allo scopo di risolvere i sistemi integrabili. Vengono descritte le funzioni ellittiche, in particolare la funzione ellittica di Weierstrass, ed elenchiamo i tipi di integrali ellittici costruendoli dalle funzioni di Weierstrass. Dopo aver considerato le basi della meccanica Hamiltoniana ed il teorema di Arnold Liouville, studiamo un esempio preso dal libro di Moser-Integrable Hamiltonian Systems and Spectral Theory, dove si prendono in considerazione i sistemi integrabili lungo la geodetica di un'ellissoide, e il sistema di Von Neumann. In particolare vediamo che nel caso n=2 abbiamo un integrale ellittico.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

An implicit method for the solution of elliptic partial differential equations.

Supported in part by National Science Foundation under Grant No. U.S. NSF-GJ-328.