Besov spaces, Sobolev spaces, and Cauchy integrals.
نویسندگان
چکیده
منابع مشابه
Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains
Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of developing a similar sharp theory for semilinear problems of the type ∆u − N(x, u) = F (x), equipped with Dirichlet and Neumann boundary conditions.
متن کاملThe Cauchy Problem for Semilinear Parabolic Equations in Besov Spaces
In this paper we first give a unified method by introducing the concept of admissible triplets to study local and global Cauchy problems for semi-linear parabolic equations with a general nonlinear term in different Sobolev spaces. In particular, we establish the local well-posedness and small global well-posedness of the Cauchy problem for semi-linear parabolic equations without the homogeneou...
متن کاملCirculation integrals and critical Sobolev spaces : problems of optimal constants
We study various questions related to the best constants in the following inequalities established in [1, 2, 3]; ̨̨̨Z Γ ~ φ · ~t ̨̨̨ ≤ Cn‖∇φ‖Ln |Γ| , and ̨̨̨Z Rn ~ φ · ~ μ ̨̨̨ ≤ Cn‖∇φ‖Ln‖~ μ‖ , where Γ is a closed curve in Rn, ~ φ ∈ C∞ c (Rn; Rn) and ~ μ is a bounded measure on Rn with values into Rn such that div ~ μ = 0. In 2d the answers are rather complete and closely related to the best constants for ...
متن کاملBoundedness of Oscillatory Singular Integrals on Weighted Sobolev Spaces
In this paper, an oscillatory singular integral operator T deened by T f (x) = Z IR e ixP(y) f (x ? y) y dy is showed to be bounded on a weighted Sobolev space H
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1992
ISSN: 0026-2285
DOI: 10.1307/mmj/1029004520