Search results for "bound"
showing 10 items of 2948 documents
Solvability of the divergence equation implies John via Poincaré inequality
2014
Abstract Let Ω ⊂ R 2 be a bounded simply connected domain. We show that, for a fixed (every) p ∈ ( 1 , ∞ ) , the divergence equation div v = f is solvable in W 0 1 , p ( Ω ) 2 for every f ∈ L 0 p ( Ω ) , if and only if Ω is a John domain, if and only if the weighted Poincare inequality ∫ Ω | u ( x ) − u Ω | q d x ≤ C ∫ Ω | ∇ u ( x ) | q dist ( x , ∂ Ω ) q d x holds for some (every) q ∈ [ 1 , ∞ ) . This gives a positive answer to a question raised by Russ (2013) in the case of bounded simply connected domains. In higher dimensions similar results are proved under some additional assumptions on the domain in question.
Isometries between spaces of multiple Dirichlet series
2019
Abstract In this paper we study spaces of multiple Dirichlet series and their properties. We set the ground of the theory of multiple Dirichlet series and define the spaces H ∞ ( C + k ) , k ∈ N , of convergent and bounded multiple Dirichlet series on C + k . We give a representation for these Banach spaces and prove that they are all isometrically isomorphic, independently of the dimension. The analogous result for A ( C + k ) , k ∈ N , which are the spaces of multiple Dirichlet series that are convergent on C + k and define uniformly continuous functions, is obtained.
Errors Generated by Uncertain Data
2014
In this chapter, we study effects caused by incompletely known data. In practice, the data are never known exactly, therefore the results generated by a mathematical model also have a limited accuracy. Then, the whole subject of error analysis should be treated in a different manner, and accuracy of numerical solutions should be considered within a framework of a more complicated scheme, which includes such notions as maximal and minimal distances to the solution set and its radius.
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.
Functional inequalities for generalized inverse trigonometric and hyperbolic functions
2014
Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Gr\"unbaum inequalities with the aid of the classical Bernoulli inequality. Moreover, by means of certain already derived bounds, bilateral bounding inequalities are obtained for the generalized hypergeometric ${}_3F_2$ Clausen function.
On elliptic equations involving the 1-Laplacian operator
2018
El objetivo de esta tesis doctoral es dar a conocer los resultados obtenidos sobre existencia, unicidad y regularidad de las soluciones de diferentes ecuaciones elípticas regidas por el operador 1-laplaciano. El primer capítulo está dedicado al estudio de la ecuación - div (Du/|Du|) + g(u) |Du| = f(x) en un subconjunto abierto y acotado U de R^N con frontera Lipschitz, con la condición de Dirichlet u=0 en la frontera, tomando una función f positiva y siendo g una función real, continua y positiva. Por un lado, obtenemos soluciones no acotadas cuando el dato f pertenece al espacio de Marcinkiewicz L^{N,\infty}(U), por lo que debemos introducir la definición apropiada para este tipo de soluci…
Imagine there’s no borders. Miti identitari, percorsi di viaggio, sguardi sull’altro dall’Antichità al Medioevo
2022
Sulla dicotomia identità e alterità la critica moderna si è molto esercitata negli ultimi decenni, mettendo a punto un armamentario di strumenti e categorie analitiche utili a identificarne i rispettivi spazi di applicazione: da un lato, troviamo dunque l’identità, con tutto il suo repertorio di parole-chiave, quali tradizione, memoria, scrittura, purezza, coerenza; dall’altro, l’alterità, in tutti i suoi gradi, che vanno da una potenziale assimilabilità a un’estraneità radicale, espressa, volta per volta, dalla climax di termini quali ospite, straniero, rifugiato politico, esiliato, nemico, invasore. Il volume che qui presentiamo si propone di indagare, attraverso una galleria di casi stud…
Optimization of trigeneration systems by Mathematical Programming: influence of plant scheme and boundary conditions
2014
The large potential for energy saving by cogeneration and trigeneration in the building sector is scarcely exploited due to a number of obstacles in making the investment attractive. The analyst often encounters difficulties in identifying optimal design and operation strategies, since a number of factors, either endogenous (i.e. related with the energy load profiles) and exogenous (i.e. related with external conditions like energy prices and support mechanisms), influence the economic viability. In this paper a decision tool is presented, that simultaneously optimizes the plant lay-out, the sizes of the main components and their operation strategy. For a specific building in the hotel sect…
Positive solutions for nonlinear Robin problems
2017
We consider a parametric Robin problem driven by the p-Laplacian with an indefinite potential and with a superlinear reaction term which does not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions. We prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies. We also show the existence of a minimal positive solution $\tilde{u}_\lambda$ and establish the monotonicity and continuity of the map $\lambda\to \tilde{u}_\lambda$.
Praca nad własną biografią matek dzieci z niepełnosprawnością na przykładzie projektu pt. „Siła kobiet”
2021
W artykule opisany został projekt edukacyjno-socjalny pt. ,,Siła kobiet", skierowany do matek dzieci z niepełnosprawnością. Projekt miał tez charakter naukowo-badawczy, którego nadrzędnym celem było poznanie procesu uczenia się z biografii. Intencją autorki było zaprezentowanie działań realizowanych podczas projektu, które miały umożliwić jego uczestniczkom zaobserwowanie procesu uczenia się z własnej biografii w kontekście niepełnosprawności swojego dziecka. W pierwszej części artykułu zamieszczony został teoretyczno-metodologiczny opis projektu i jego metodyczne podstawy. W części analitycznej zaprezentowane zostały fragmenty transkrypcji w odniesieniu do teorii uczenia się sytuacyjnego i…