A Sobolev-type inequality for the curl operator and ground states for the curl-curl equation with critical Sobolev exponent

DOI10.1007/S00205-021-01684-XzbMath1475.35332arXiv2002.00613OpenAlexW3170378729MaRDI QIDQ2043052

Andrzej Szulkin, Jarosław Mederski

Publication date: 22 July 2021

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00613

zbMATH Keywords

curl-curl equation

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Navier-Stokes equations (35Q30) NLS equations (nonlinear Schrödinger equations) (35Q55) Electromagnetic theory (general) (78A25) Variational methods for second-order elliptic equations (35J20) Inequalities involving derivatives and differential and integral operators (26D10) Maxwell equations (35Q61)

Related Items (5)

Cylindrically symmetric solutions of curl-curl equation with nonlocal nonlinearity ⋮ Multiple Solutions to Cylindrically Symmetric Curl-Curl Problems and Related Schrödinger Equations with Singular Potentials ⋮ Ground state solution of weakly coupled time-harmonic Maxwell equations ⋮ Multiple cylindrically symmetric solutions of nonlinear Maxwell equations ⋮ Nonlinear curl-curl problems in $\mathbb{R}^3$

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