The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary

Arrieta Algarra, José MaríaRodríguez Bernal, AníbalRossi, Julio D.2023-06-202023-06-2020080308-210510.1017/S0308210506000813https://hdl.handle.net/20.500.14352/49743In this paper we prove that the best constant in the Sobolev trace embedding H1() ,! Lq(@) in a bounded smooth domain can be obtained as the limit as " ! 0 of the best constant of the usual Sobolev embedding H1() ,! Lq(!", dx/") where !" = {x 2 : dist(x, @) < "} is a small neighborhood of the boundary. We also analyze symmetry properties of extremals of this last embedding when is a ball.engThe best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundaryjournal articlehttp://journals.cambridge.org/action/displayJournal?jid=PRMopen access517.9Nonlinear boundary conditionsSobolev trace embeddingSymmetry of extremalsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias