Cutting the loss of derivatives for solvability under condition $(\Psi )$

Nicolas Lerner

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Displaying similar documents to “Cutting the loss of derivatives for solvability under condition $(Ψ)$ ”

Some results on spaces with $ℵ_{1}$ -calibre

Wei-Feng Xuan, Wei-Xue Shi (2016)

Commentationes Mathematicae Universitatis Carolinae

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We prove that, assuming , if $X$ is a space with $ℵ_{1}$ -calibre and a zeroset diagonal, then $X$ is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular $G_{δ}$ -diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. We also make some observations on spaces with $ℵ_{1}$ -calibre.

Coincidence for substitutions of Pisot type

Marcy Barge, Beverly Diamond (2002)

Bulletin de la Société Mathématique de France

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Let $ϕ$ be a substitution of Pisot type on the alphabet $𝒜 = {1, 2, ..., d}$ ; $ϕ$ satisfies theif for every $i, j \in 𝒜$ , there are integers $k, n$ such that $ϕ^{n} (i)$ and $ϕ^{n} (j)$ have the same $k$ -th letter, and the prefixes of length $k - 1$ of $ϕ^{n} (i)$ and $ϕ^{n} (j)$ have the same image under the abelianization map. We prove that the strong coincidence condition is satisfied if $d = 2$ and provide a partial result for $d \geq 2$ .

On multiset colorings of generalized corona graphs

Yun Feng, Wensong Lin (2016)

Mathematica Bohemica

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A vertex $k$ -coloring of a graph $G$ is a if $M (u) \neq M (v)$ for every edge $u v \in E (G)$ , where $M (u)$ and $M (v)$ denote the multisets of colors of the neighbors of $u$ and $v$ , respectively. The minimum $k$ for which $G$ has a multiset $k$ -coloring is the $χ_{m} (G)$ of $G$ . For an integer $ℓ \geq 0$ , the $ℓ$ - of a graph $G$ , ${cor}^{ℓ} (G)$ , is the graph obtained from $G$ by adding, for each vertex $v$ in $G$ , $ℓ$ new neighbors which are end-vertices. In this paper, the multiset chromatic numbers are determined for $ℓ$ - of all complete graphs, the regular complete...

Local-global divisibility of rational points in some commutative algebraic groups

Roberto Dvornicich, Umberto Zannier (2001)

Bulletin de la Société Mathématique de France

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Let $𝒜$ be a commutative algebraic group defined over a number field $k$ . We consider the following question:A complete answer for the case of the multiplicative group $𝔾_{m}$ is classical. We study other instances and in particular obtain an affirmative answer when $r$ is a prime and $𝒜$ is either an elliptic curve or a torus of small dimension with respect to $r$ . Without restriction on the dimension of a torus, we produce an example showing that the answer can be negative even when $r$ is a prime. ...

The parabolic Anderson model in a dynamic random environment: Basic properties of the quenched Lyapunov exponent

D. Erhard, F. den Hollander, G. Maillard (2014)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper we study the parabolic Anderson equation $\partial u (x, t) / \partial t = κ 𝛥 u (x, t) + ξ (x, t) u (x, t)$ , $x \in ℤ^{d}$ , $t \geq 0$ , where the $u$ -field and the $ξ$ -field are $ℝ$ -valued, $κ \in [0, \infty)$ is the diffusion constant, and $𝛥$ is the discrete Laplacian. The $ξ$ -field plays the role of athat drives the equation. The initial condition $u (x, 0) = u_{0} (x)$ , $x \in ℤ^{d}$ , is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate $2 d κ$ ,...

On standard norm varieties

Nikita A. Karpenko, Alexander S. Merkurjev (2013)

Annales scientifiques de l'École Normale Supérieure

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Let $p$ be a prime integer and $F$ a field of characteristic $0$ . Let $X$ be theof a symbol in the Galois cohomology group $H^{n + 1} (F, μ_{p}^{\otimes n})$ (for some $n \geq 1$ ), constructed in the proof of the Bloch-Kato conjecture. The main result of the paper affirms that the function field $F (X)$ has the following property: for any equidimensional variety $Y$ , the change of field homomorphism $CH (Y) \to CH (Y_{F (X)})$ of Chow groups with coefficients in integers localized at $p$ is surjective in codimensions $< (dim X) / (p - 1)$ . One of the main ingredients of the proof is a computation...

G-tridiagonal majorization on $𝐌_{n, m}$

Ahmad Mohammadhasani, Yamin Sayyari, Mahdi Sabzvari (2021)

Communications in Mathematics

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For $X, Y \in 𝐌_{n, m}$ , it is said that $X$ is majorized by $Y$ (and it is denoted by $X ≺_{g t} Y$ ) if there exists a tridiagonal g-doubly stochastic matrix $A$ such that $X = A Y$ . In this paper, the linear preservers and strong linear preservers of $≺_{g t}$ are characterized on $𝐌_{n, m}$ .

The equation $- Δ 𝑢 - λ \frac{𝑢}{{| 𝑥 |}^{2}} = {| \nabla 𝑢 |}^{𝑝} + 𝑐 𝑓 (𝑥)$ : The optimal power

Boumediene Abdellaoui, Ireneo Peral (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We will consider the following problem $- Δ u - λ \frac{u}{{| x |}^{2}} = {| \nabla u |}^{p} + c f, u > 0 in Ω,$ where $Ω \subset ℝ^{N}$ is a domain such that $0 \in Ω$ , $N \geq 3$ , $c > 0$ and $λ > 0$ . The main objective of this note is to study the precise threshold $p_{+} = p_{+} (λ)$ for which there is novery weak supersolutionif $p \geq p_{+} (λ)$ . The optimality of $p_{+} (λ)$ is also proved by showing the solvability of the Dirichlet problem when $1 \leq p < p_{+} (λ)$ , for $c > 0$ small enough and $f \geq 0$ under some hypotheses that we will prescribe.

A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type

Soohyun Bae (2023)

Archivum Mathematicum

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We consider the quasilinear equation $Δ_{p} u + K (| x |) u^{q} = 0$ , and present the proof of the local existence of positive radial solutions near $0$ under suitable conditions on $K$ . Moreover, we provide a priori estimates of positive radial solutions near $\infty$ when $r^{- ℓ} K (r)$ for $ℓ \geq - p$ is bounded near $\infty$ .

Thompson’s conjecture for the alternating group of degree $2 p$ and $2 p + 1$

Azam Babai, Ali Mahmoudifar (2017)

Czechoslovak Mathematical Journal

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For a finite group $G$ denote by $N (G)$ the set of conjugacy class sizes of $G$ . In 1980s, J. G. Thompson posed the following conjecture: If $L$ is a finite nonabelian simple group, $G$ is a finite group with trivial center and $N (G) = N (L)$ , then $G ≅ L$ . We prove this conjecture for an infinite class of simple groups. Let $p$ be an odd prime. We show that every finite group $G$ with the property $Z (G) = 1$ and $N (G) = N (A_{i})$ is necessarily isomorphic to $A_{i}$ , where $i \in {2 p, 2 p + 1}$ .

On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

$𝒞^{k}$ -regularity for the $\bar{\partial}$ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let $D$ be a $𝒞^{d}$ $q$ -convex intersection, $d \geq 2$ , $0 \leq q \leq n - 1$ , in a complex manifold $X$ of complex dimension $n$ , $n \geq 2$ , and let $E$ be a holomorphic vector bundle of rank $N$ over $X$ . In this paper, $𝒞^{k}$ -estimates, $k = 2, 3, \dots, \infty$ , for solutions to the $\bar{\partial}$ -equation with small loss of smoothness are obtained for $E$ -valued $(0, s)$ -forms on $D$ when $n - q \leq s \leq n$ . In addition, we solve the $\bar{\partial}$ -equation with a support condition in $𝒞^{k}$ -spaces. More precisely, we prove that for a $\bar{\partial}$ -closed form $f$ in $𝒞_{0, q}^{k} (X ∖ D, E)$ , $1 \leq q \leq n - 2$ , $n \geq 3$ , with compact support and for $ε$ with $0 < ε < 1$ there...

Displaying similar documents to “Cutting the loss of derivatives for solvability under condition ( Ψ ) ”

Displaying similar documents to “Cutting the loss of derivatives for solvability under condition $(Ψ)$ ”