RT Journal Article
T1 On the Dirichlet problem on Lorentz and Orlicz spaces with applications to Schwarz-Christoffel domains
A1 Carro Rossell, María Jesús
A1 Ortiz Caraballo, Carmen
AB It is known (see [14]) that, for every Lipschitz domain  on the plane  Ω = {x + iy : y > ν(x)}, with ν a real valued Lipschitz function, there exists 1 ≤ p0 < 2 so that the Dirichlet problem has a solution for every function f ∈ Lp(ds) and every p ∈ (p0,∞). Moreover, if p0 > 1, the result is false for every p ≤ p0. The purpose of this paper is to study in more detail what happens at the endpoint p0; that is, we want to find spaces X ⊂ Lp0 so that the Dirichlet problem is solvable for every f ∈ X. These spaces X will be either the Lorentz space Lp0,1(ds) or some type of logarithmic Orlicz space. Our results will be applied to the special case of Schwarz–Christoffel Lipschitz domains, among others, for which we explicitly compute the value of p0.
PB Elsevier
SN 1090-2732
YR 2018
FD 2018
LK https://hdl.handle.net/20.500.14352/93676
UL https://hdl.handle.net/20.500.14352/93676
LA eng
NO M.J. Carro, C. Ortiz-Caraballo, On the Dirichlet problem on Lorentz and Orlicz spaces with applications to Schwarz–Christoffel domains, Journal of Differential Equations 265 (2018) 2013–2033. https://doi.org/10.1016/j.jde.2018.04.028.
NO Ministerio de Economía, Comercio y Empresa (España)
DS Docta Complutense
RD 14 dic 2025