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Indices of Orlicz spaces and some applications

Alberto Fiorenza, Miroslav Krbec (1997)

Commentationes Mathematicae Universitatis Carolinae

We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.

Infinitely many periodic solutions for variable exponent systems.

Guo, Xiaoli, Lu, Mingxin, Zhang, Qihu (2009)

Journal of Inequalities and Applications [electronic only]

Infinitely many periodic solutions of nonlinear wave equations on $S^{n}$ .

Kim, Jintae (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Invariant measures for Burgers equation with stochastic forcing.

E, Weinan, Khanin, K., Mazel, A., Sinai, Ya. (2000)

Annals of Mathematics. Second Series

Invariant regions associated with quasilinear damped wave equations

Eduard Feireisl (1990)

Czechoslovak Mathematical Journal

Invariant sets for nonlinear evolution equations, Cauchy problems and periodic problems.

Hirano, Norimichi, Shioji, Naoki (2004)

Abstract and Applied Analysis

Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS

Andrea R. Nahmod, Tadahiro Oh, Luc Rey-Bellet, Gigliola Staffilani (2012)

Journal of the European Mathematical Society

We construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost surely for data in a Fourier–Lebesgue space $ℱ L^{s, r} (T)$ with $s \geq \frac{1}{2}, 2 < r < 4, (s - 1) r < - 1$ and scaling like $H^{\frac{1}{2} - ϵ} (𝕋)$ , for small $ϵ > 0$ . We also show the invariance of this measure.