کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8898627 1631493 2013 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the Dirichlet problem on Lorentz and Orlicz spaces with applications to Schwarz-Christoffel domains
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
On the Dirichlet problem on Lorentz and Orlicz spaces with applications to Schwarz-Christoffel domains
چکیده انگلیسی
It is known (see [14]) that, for every Lipschitz domain Ω on the planeΩ={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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 265, Issue 5, 5 September 2018, Pages 2013-2033
نویسندگان
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