Ground States of Time-Harmonic Semilinear Maxwell Equations in $${\mathbb{R}^3}$$ R 3 with Vanishing Permittivity
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| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151101xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-015-0870-1 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0870-1 | ||
| 100 | 1 | |a Mederski |D Jarosław |u Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland |4 aut | |
| 245 | 1 | 0 | |a Ground States of Time-Harmonic Semilinear Maxwell Equations in $${\mathbb{R}^3}$$ R 3 with Vanishing Permittivity |h [Elektronische Daten] |c [Jarosław Mederski] |
| 520 | 3 | |a We investigate the existence of solutions $${E:\mathbb{R}^3 \to \mathbb{R}^3}$$ E : R 3 → R 3 of the time-harmonic semilinear Maxwell equation $$\nabla \times (\nabla \times E) + V(x) E = \partial_E F(x, E) \quad {\rm in} \mathbb{R}^3$$ ∇ × ( ∇ × E ) + V ( x ) E = ∂ E F ( x , E ) in R 3 where $${V:\mathbb{R}^3 \to \mathbb{R}}$$ V : R 3 → R , $${V(x) \leqq 0}$$ V ( x ) ≦ 0 almost everywhere on $${\mathbb{R}^3}$$ R 3 , $${\nabla \times}$$ ∇ × denotes the curl operator in $${\mathbb{R}^3}$$ R 3 and $${F:\mathbb{R}^3 \times \mathbb{R}^3 \to \mathbb{R}}$$ F : R 3 × R 3 → R is a nonlinear function in E. In particular we find a ground state solution provided that suitable growth conditions on F are imposed and the $${L^{3/2}}$$ L 3 / 2 -norm of V is less than the best Sobolev constant. In applications, F is responsible for the nonlinear polarization and $${V(x) = -\mu\omega^2 \varepsilon(x)}$$ V ( x ) = - μ ω 2 ε ( x ) whereμ>0 is the magnetic permeability, ω is the frequency of the time-harmonic electric field $${\mathfrak{R}\{E(x){\rm e}^{i\omega t}\}}$$ R { E ( x ) e i ω t } and $${\varepsilon}$$ ε is the linear part of the permittivity in an inhomogeneous medium. | |
| 540 | |a The Author(s), 2015 | ||
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 825-861 |x 0003-9527 |q 218:2<825 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0870-1 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0870-1 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Mederski |D Jarosław |u Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 825-861 |x 0003-9527 |q 218:2<825 |1 2015 |2 218 |o 205 | ||