On the algebraic properties of the $H_{\frac{n}{2},{\frac{1}{2}}}$ spaces

Sergiu Klainerman; Matei Machedon

Displaying similar documents to “On the algebraic properties of the $H_{\frac{n}{2}, \frac{1}{2}}$ spaces”

Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $L^{1} (Ω)$

M. F. Betta, A. Mercaldo, F. Murat, M. M. Porzio (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we prove uniqueness results for the renormalized solution, if it exists, of a class of non coercive nonlinear problems whose prototype is $\{\begin{matrix} - div (a (x) (1 + {| \nabla u |}^{2})^{\frac{p - 2}{2}} {\nabla u) + b (x) (1 + | \nabla u |}^{2})^{\frac{λ}{2}} = f & in Ω, \\ u = 0 & on \partial Ω, \end{matrix}$ where $Ω$ is a bounded open subset of $ℝ^{N}$ , $N \geq 2$ , $2 - 1 / N < p < N$ , $a$ belongs to $L^{\infty} (Ω)$ , $a (x) \geq α_{0} > 0$ , $f$ is a function in $L^{1} (Ω)$ , $b$ is a function in $L^{r} (Ω)$ and $0 \leq λ < λ^{*} (N, p, r),$ for some $r$ and $λ^{*} (N, p, r)$ .

Spaces of continuous functions, $Σ$ -products and Box Topology

J. Angoa, Angel Tamariz-Mascarúa (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

For a Tychonoff space $X$ , we will denote by $X_{0}$ the set of its isolated points and $X_{1}$ will be equal to $X ∖ X_{0}$ . The symbol $C (X)$ denotes the space of real-valued continuous functions defined on $X$ . $□ ℝ^{κ}$ is the Cartesian product $ℝ^{κ}$ with its box topology, and $C_{□} (X)$ is $C (X)$ with the topology inherited from $□ ℝ^{X}$ . By $\hat{C} (X_{1})$ we denote the set ${f \in C (X_{1}) : f$ can be continuously extended to all of $X}$ . A space $X$ is almost- $ω$ -resolvable if it can be partitioned by a countable family of subsets in such a way that every non-empty open subset of...

Unique continuation for the solutions of the laplacian plus a drift

Alberto Ruiz, Luis Vega (1991)

Annales de l'institut Fourier

Similarity:

We prove unique continuation for solutions of the inequality $| Δ u (x) | \leq V (x) | \nabla u (x) |$ , $x \in Ω$ a connected set contained in $R^{n}$ and $V$ is in the Morrey spaces $F^{α, p}$ , with $p \geq (n - 2) / 2 (1 - α)$ and $α < 1$ . These spaces include $L^{q}$ for $q \geq (3 n - 2) / 2$ (see [H], [BKRS]). If $p = (n - 2) / 2 (1 - α)$ , the extra assumption of $V$ being small enough is needed.

Existence and regularity of solutions of the $\bar{δ}$ -system on wedges of $C^{N}$

Giuseppe Zampieri (1999)

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

Similarity:

For a wedge $W$ of $C^{N}$ , we introduce two conditions of weak $q$ -pseudoconvexity, and prove that they entail solvability of the $\bar{δ}$ -system for forms of degree $\geq q + 1$ with coefficients in $C^{\infty} (W)$ and $C^{\infty} (\bar{W})$ respectively. Existence and regularity for $\bar{δ}$ in $W$ is treated by Hörmander [5, 6] (and also by Zampieri [9, 11] in case of piecewise smooth boundaries). Regularity in $W$ is treated by Henkin [4] (strong $q$ -pseudoconvexity by the method of the integral representation), Dufresnoy [3] (full pseudoconvexity), Michel...

Large data local solutions for the derivative NLS equation

Ioan Bejenaru, Daniel Tataru (2008)

Journal of the European Mathematical Society

Similarity:

We consider the derivative NLS equation with general quadratic nonlinearities. In [2] the first author has proved a sharp small data local well-posedness result in Sobolev spaces with a decay structure at infinity in dimension $n = 2$ . Here we prove a similar result for large initial data in all dimensions $n \geq 2$ .

Bond ionization energies: thiophosphoryl compounds

Marco V. Andreocci, Carla Cauletti, Claudio Furlani (1977)

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

Similarity:

Negli spettri fotoelettronici (p.e.) indotti da radiazione ultra-violetta di serie omologhe di composti, si trovano bande in ben definite regioni di energia, che possono essere assegnate empiricamente a ionizzazione di legami specifici o di coppie solitarie di elettroni. L’effetto dell'intorno chimico sulle energie di ionizzazione si esplica in piccoli spostamenti, che hanno una dipendenza approssimativamente lineare dall'ettronegatività di atomi o gruppi vicini. La discussione riguarda...

Explicit form for the discrete logarithm over the field $GF (p, k)$

Gerasimos C. Meletiou (1993)

Archivum Mathematicum

Similarity:

For $a$ generator of the multiplicative group of the field $G F (p, k)$ , the discrete logarithm of an element $b$ of the field to the base $a$ , $b \neq 0$ is that integer $z : 1 \leq z \leq p^{k} - 1$ , $b = a^{z}$ . The $p$ -ary digits which represent $z$ can be described with extremely simple polynomial forms.

On the Cauchy problem in linear viscoelasticity

Pasquale Renno (1983)

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

Similarity:

Con riferimento all’operatore integrodifferenziale della viscoelasticità lineare nella formulazione creep, si determina la soluzione fondamentale $E$ in corrispondenza di un’arbitraria funzione di memoria. Di conseguenza viene risolto esplicitamente il problema di Cauchy relativo al moto unidimensionale di un sistema viscoelastico $\mathcal{B}$ , omogeneo ed isotropo, determinato da dati iniziali e storia di stress comunque prefissati. Successivamente, nell’ambito di opportune ipotesi di memoria labile,...

Displaying similar documents to “On the algebraic properties of the H n 2 , 1 2 spaces”

Displaying similar documents to “On the algebraic properties of the $H_{\frac{n}{2}, \frac{1}{2}}$ spaces”