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Method of fundamental solutions for biharmonic equation based on Almansi-type decomposition

Koya Sakakibara (2017)

Applications of Mathematics

The aim of this paper is to analyze mathematically the method of fundamental solutions applied to the biharmonic problem. The key idea is to use Almansi-type decomposition of biharmonic functions, which enables us to represent the biharmonic function in terms of two harmonic functions. Based on this decomposition, we prove that an approximate solution exists uniquely and that the approximation error decays exponentially with respect to the number of the singular points. We finally present results...

Multifractals and projections.

Fadhila Bahroun, Imen Bhouri (2006)

Extracta Mathematicae

In this paper, we generalize the result of Hunt and Kaloshin [5] about the Lq-spectral dimensions of a measure and that of its projections. The results we obtain, allow to study an untreated case in their work and to find a relationship between the multifractal spectrum of a measure and that of its projections.

Multiplicative square functions.

María José González, Artur Nicolau (2004)

Revista Matemática Iberoamericana

We study regularity properties of a positive measure in the euclidean space in terms of two square functions which are the multiplicative analogues of the usual martingale square function and of the Lusin area function of a harmonic function. The size of ...

Negligible sets and good functions on polydiscs

Kohur Gowrisankaran (1979)

Annales de l'institut Fourier

A notion of negligible sets for polydiscs is introduced. Some properties of non-negligible sets are proved. These results are used to construct good and good inner functions on polydiscs.

Nonbasic harmonic maps onto convex wedges

Josephi Cima, Alberti Livingston (1993)

Colloquium Mathematicae

We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation f z ¯ = a f z where a(z) is a nontrivial extreme point of the unit ball of H ∞ .

Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population

Afif Amar (2011)

Open Mathematics

Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary value problem arising in the theory of growing cell population in L 1-setting. Besides, a topological structure of the set of solutions is provided.

Non-subharmonicity of the Hausdorff distance

Edoardo Vesentini (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dimostra con esempi che la distanza di Hausdorff-Carathéodory fra i valori di funzioni multivoche, analitiche secondo Oka, non è subarmonica.

Numerical analysis of the general biharmonic problem by the finite element method

Jiří Hřebíček (1982)

Aplikace matematiky

The present paper deals with solving the general biharmonic problem by the finite element method using curved triangular finit C 1 -elements introduced by Ženíšek. The effect of numerical integration is analysed in the case of mixed boundary conditions and sufficient conditions for the uniform V O h -ellipticity are found.

Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials

Liubov Efremova, Gerhard Freiling (2013)

Open Mathematics

We consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.

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