Articles
8.
Maximum principles for some quasilinear elliptic systems
Leonardi, Salvatore and Leonetti, Francesco and Pignotti, Cristina and Rocha, Eugénio and Staicu, Vasile
Nonlinear Analysis: Theory, Methods and Applications
Elsevier
We give maximum principles for solutions u:Ω→ℝ N to a class of quasilinear elliptic systems whose prototype is [Formula presented]where α∈{1,…,N} is the equation index and Ω is an open, bounded subset of ℝ n . We assume that coefficients [Formula presented] are measurable with respect to x, continuous with respect to y∈ℝ N , bounded and elliptic. In vectorial problems, when trying to bound the solution by means of the boundary data, we need to bypass De Giorgi's counterexample by means of some additional structure assumptions on the coefficients [Formula presented]. In this paper, we assume that offdiagonal coefficients [Formula presented], α≠β, have support in some staircase set along the diagonal in the y α ,y β plane
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7.
Variable exponent BesovMorrey spaces
Almeida, Alexandre and Caetano, António
Journal of Fourier Analysis and Applications
Springer Verlag
In this paper we introduce BesovMorrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of nonstandard function spaces requires the introduction of variable exponent mixed Morreysequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.
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6.
Maximal commutators and commutators of potential operators in new vanishing Morrey spaces
Almeida, Alexandre
Nonlinear Analysis
Elsevier
We study mapping properties of commutators in certain vanishing subspaces of Morrey spaces, which were recently used to solve the delicate problem of describing the closure of nice functions in Morrey norm. We show that the vanishing properties defining those subspaces are preserved under the action of maximal commutators and commutators of fractional integral operators.
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5.
On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
Alabalik, Aysegul Ç. and Almeida, Alexandre and Samko, Stefan
Banach Journal of Mathematical Analysis
Springer
We consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of C∞0(Rn) in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the Hardy–Littlewood maximal operator, singular type operators and Hardy operators. We also show that the vanishing properties defining those subspaces are preserved under the action of Riesz potential operators and fractional maximal operators.
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4.
Decompositions with atoms and molecules for variable exponent TriebelLizorkinMorrey spaces
Caetano, António and Kempka, Henning
Constructive Approximation
Springer Verlag
We continue the study of the variable exponent Morreyﬁed TriebelLizorkin spaces introduced in a previous paper. Here we give characterizations by means of atoms and molecules. We also show that in some cases the number of zero moments needed for molecules, in order that an inﬁnite linear combination of them (with coeﬃcients in a natural sequence space) converges in the space of tempered distributions, is much smaller than what is usually required.
We also establish a Sobolev type theorem for related sequence spaces, which might have independent interest.
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3.
Variable exponent TriebelLizorkinMorrey spaces
Caetano, António and Kempka, Henning
Journal of Mathematical Analysis and Applications
Elsevier
We introduce variable exponent versions of Morreyﬁed TriebelLizorkin spaces. To that end, we prove an important convolution inequality which is a replacement for the HardyLittlewood maximal inequality in the fully variable setting. Using it we obtain characterizations by means of Peetre maximal functions and use them to show the independence of the introduced spaces from the admissible system used.
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2.
New convolutions and their applicability to integral equations of WienerHopf plus Hankel type
Castro, Luis P. and Guerra, Rita C. and Tuan, Nguyen Minh
Mathematical Methods in the Applied Sciences
Wiley
We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fouriertype together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of WienerHopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fouriertype series are used to produce the solution formula of such equations and a Shannontype sampling formula is also obtained.
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1.
Mixed impedance boundary value problems for the Laplace–Beltrami equation
Castro, Luis and Duduchava, Roland and Speck, FrankOlme
Journal of Integral Equations and Applications
Rocky Mountain Mathematics Consortium
This work is devoted to the analysis of the mixed impedanceNeumannDirichlet boundary value problem (MIND~BVP) for the LaplaceBeltrami equation on a compact smooth surface $mathcal{C}$ with smooth boundary. We prove, using the LaxMilgram Lemma, that this MIND BVP has a unique solution in the classical weak setting $mathbb{H}^1(mathcal{C})$ when considering positive constants in the impedance condition. The main purpose is to consider the MIND~BVP in a nonclassical setting of the Bessel potential space $mathbb{H}^s_p(mathcal{C})$, for $s> 1/p$, $1
1/p$ and $1
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