Zobrazeno 1 - 10
of 64
pro vyhledávání: '"Kunstmann, Peer Christian"'
Publikováno v:
Nonlinear Differ. Equ. Appl. 28, 11 (2021)
We study the one dimensional nonlinear Schr\"odinger equation with power nonlinearity $|u|^{\alpha - 1} u$ for $\alpha \in [1,5]$ and initial data $u_0 \in L^2(\mathbb{R}) + H^1(\mathbb{T})$. We show via Strichartz estimates that the Cauchy problem i
Externí odkaz:
http://arxiv.org/abs/1904.04030
Akademický článek
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Publikováno v:
D\"orfler W. et al. (eds) Mathematics of Wave Phenomena. Trends in Mathematics. Birkh\"auser, Cham. 2020
We introduce a Littlewood-Paley characterization of modulation spaces and use it to give an alternative proof of the algebra property, somehow implicitly contained in Sugimoto (2011), of the intersection $M^s_{p,q}(\mathbb{R}^d) \cap M_{\infty, 1}(\m
Externí odkaz:
http://arxiv.org/abs/1610.08298
A result by Liskevich and Perelmuter from 1995 yields the optimal angle of analyticity for symmetric submarkovian semigroups on $L_p$, $1
Externí odkaz:
http://arxiv.org/abs/1603.08862
We show results on $L^p$-spectral multipliers for Maxwell operators with bounded measurable coefficients. We also present similar results for the Stokes operator with Hodge boundary conditions and the Lam\'e system. Here we rely on resolvent estimate
Externí odkaz:
http://arxiv.org/abs/1209.0694
Let $X$ be a space of homogeneous type and let $L$ be an injective, non-negative, self-adjoint operator on $L^2(X)$ such that the semigroup generated by $-L$ fulfills Davies-Gaffney estimates of arbitrary order. We prove that the operator $F(L)$, ini
Externí odkaz:
http://arxiv.org/abs/1209.0358
We introduce a notion of generalized Triebel-Lizorkin spaces associated with sectorial operators in Banach function spaces. Our approach is based on holomorphic functional calculus techniques. Using the concept of $\mathcal{R}_s$-sectorial operators,
Externí odkaz:
http://arxiv.org/abs/1207.4217
Let $X$ be a space of homogeneous type and let $L$ be a sectorial operator with bounded holomorphic functional calculus on $L^2(X)$. We assume that the semigroup $\{e^{-tL}\}_{t>0}$ satisfies Davies-Gaffney estimates. Associated to $L$ are certain ap
Externí odkaz:
http://arxiv.org/abs/1107.4347
We investigate Kato's method for parabolic equations with a quadratic non-linearity in an abstract form. We extract several properties known from linear systems theory which turn out to be the essential ingredients for the method. We give necessary a
Externí odkaz:
http://arxiv.org/abs/0709.2067
We study linear control systems in infinite--dimensional Banach spaces governed by analytic semigroups. For $p\in[1,\infty]$ and $\alpha\in\RR$ we introduce the notion of $L^p$--admissibility of type $\alpha$ for unbounded observation and control ope
Externí odkaz:
http://arxiv.org/abs/math/0604044