Displaying similar documents to “On the global existence for the Muskat problem”

Global analytic and Gevrey surjectivity of the Mizohata operator D 2 + i x 2 2 k D 1

Lamberto Cattabriga, Luisa Zanghirati (1990)

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

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The surjectivity of the operator D 2 + i x 2 2 k D 1 from the Gevrey space E s R 2 , s 1 , onto itself and its non-surjectivity from E s R 3 to E s R 3 is proved.

On the topology of polynomials with bounded integer coefficients

De-Jun Feng (2016)

Journal of the European Mathematical Society

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For a real number q > 1 and a positive integer m , let Y m ( q ) : = i = 0 n ϵ i q i : ϵ i 0 , ± 1 , ... , ± m , n = 0 , 1 , ... . In this paper, we show that Y m ( q ) is dense in if and only if q < m + 1 and q is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].

Geometric rigidity of × m invariant measures

Michael Hochman (2012)

Journal of the European Mathematical Society

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Let μ be a probability measure on [ 0 , 1 ] which is invariant and ergodic for T a ( x ) = a x 𝚖𝚘𝚍 1 , and 0 < 𝚍𝚒𝚖 μ < 1 . Let f be a local diffeomorphism on some open set. We show that if E and ( f μ ) E μ E , then f ' ( x ) ± a r : r at μ -a.e. point x f - 1 E . In particular, if g is a piecewise-analytic map preserving μ then there is an open g -invariant set U containing supp μ such that g U is piecewise-linear with slopes which are rational powers of a . In a similar vein, for μ as above, if b is another integer and a , b are not powers of a common integer, and if ν is...

A propagation theorem for a class of microfunctions

Andrea D&amp;#039;Agnolo, Giuseppe Zampieri (1990)

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

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Let A be a closed set of M R n , whose conormai cones x + y x * A , x A , have locally empty intersection. We first show in §1 that dist x , A , x M A is a C 1 function. We then represent the n microfunctions of C A | X , X C n , using cohomology groups of O X of degree 1. By the results of § 1-3, we are able to prove in §4 that the sections of C A | X π ˙ - 1 x 0 , x 0 A , satisfy the principle of the analytic continuation in the complex integral manifolds of H ϕ i C i = 1 , , m , ϕ i being a base for the linear hull of γ x 0 * A in T x 0 * M ; in particular we get Γ A × M T * M X C A | X A × M T ˙ * M X = 0 . When A is a half space with...

An empirical almost sure central limit theorem under the weak dependence assumptions and its application to copula processes

Marcin Dudziński (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let: 𝐘 = 𝐘 i , where 𝐘 i = Y i , 1 , . . . , Y i , d , i = 1 , 2 , , be a d -dimensional, identically distributed, stationary, centered process with uniform marginals and a joint cdf F , and F n 𝐱 : = 1 n i = 1 n 𝕀 Y i , 1 x 1 , , Y i , d x d denote the corresponding empirical cdf. In our work, we prove the almost sure central limit theorem for an empirical process B n = n F n - F under some weak dependence conditions due to Doukhan and Louhichi. Some application of the established result to copula processes is also presented.

A Hardy type inequality for W 0 m , 1 ( Ω ) functions

Hernán Castro, Juan Dávila, Hui Wang (2013)

Journal of the European Mathematical Society

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We consider functions u W 0 m , 1 ( Ω ) , where Ω N is a smooth bounded domain, and m 2 is an integer. For all j 0 , 1 k m - 1 , such that 1 j + k m , we prove that i u ( x ) d ( x ) m - j - k W 0 k , 1 ( Ω ) with k ( i u ( x ) d ( x ) m - j - k ) L 1 ( Ω ) C u W m , 1 ( Ω ) , where d is a smooth positive function which coincides with dist ( x , Ω ) near Ω , and l denotes any partial differential operator of order l .

On square functions associated to sectorial operators

Christian Le Merdy (2004)

Bulletin de la Société Mathématique de France

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We give new results on square functions x F = 0 F ( t A ) x 2 d t t 1 / 2 p associated to a sectorial operator A on L p for 1 &lt; p &lt; . Under the assumption that A is actually R -sectorial, we prove equivalences of the form K - 1 x G x F K x G for suitable functions F , G . We also show that A has a bounded H functional calculus with respect to . F . Then we apply our results to the study of conditions under which we have an estimate ( 0 | C e - t A ( x ) | 2 d t ) 1 / 2 q M x p , when - A generates a bounded semigroup e - t A on L p and C : D ( A ) L q is a linear mapping.

Existence and multiplicity of solutions for a p ( x ) -Kirchhoff type problem via variational techniques

A. Mokhtari, Toufik Moussaoui, D. O’Regan (2015)

Archivum Mathematicum

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This paper discusses the existence and multiplicity of solutions for a class of p ( x ) -Kirchhoff type problems with Dirichlet boundary data of the following form - a + b Ω 1 p ( x ) | u | p ( x ) d x div ( | u | p ( x ) - 2 u ) = f ( x , u ) , i n Ω u = 0 o n Ω , where Ω is a smooth open subset of N and p C ( Ω ¯ ) with N < p - = inf x Ω p ( x ) p + = sup x Ω p ( x ) < + , a , b are positive constants and f : Ω ¯ × is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.