On the Poisson integral for Lipschitz and $C^{1}$-domains
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 کاملBEM and the Neumann problem for the Poisson equa- tion on Lipschitz domains
The weak Neumann problem for the Poisson eqution is studied on Lipschitz domain with compact boundary using the direct integral equation method. The domain is bounded or unbounded, the boundary might be disconnected. The problem leads to a uniquely solvable integral equation in H(∂Ω). It is proved that we can get the solution of this equation using the successive approximation method. AMS class...
متن کاملThe Poisson problem for the Lamé system on low dimensional Lipschitz domains
where ν is the unit normal to ∂Ω and the superscript t indicates transposition (in this case, of the matrix ∇~u = (∂ju)j,α). Relying on the method of layer potentials and suitable Rellich-NečasPayne-Weinberger formulas, the boundary value problems (1.2)-(1.3) with ~ f = 0 and ~g ∈ L(∂Ω), 2− ε < p < 2 + ε, have been treated (in all spacedimensions) by B. Dahlberg, C.Kenig, and G.Verchota (cf. [7...
متن کاملREGULARITY AND FREE BOUNDARY REGULARITY FOR THE p LAPLACIAN IN LIPSCHITZ AND C1 DOMAINS
In this paper we study regularity and free boundary regularity, below the continuous threshold, for the p Laplace equation in Lipschitz and C domains. To formulate our results we let Ω ⊂ R be a bounded Lipschitz domain with constant M . Given p, 1 < p < ∞, w ∈ ∂Ω, 0 < r < r0, suppose that u is a positive p harmonic function in Ω ∩ B(w, 4r), that u is continuous in Ω̄ ∩ B̄(w, 4r) and u = 0 on ∆(w,...
متن کاملOn Bogovskiı̆ and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains
We study integral operators related to a regularized version of the classical Poincaré path integral and the adjoint class generalizing Bogovskiı̆’s integral operator, acting on differential forms in R. We prove that these operators are pseudodifferential operators of order −1. The Poincaré-type operators map polynomials to polynomials and can have applications in finite element analysis. For a ...
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: Studia Mathematica
سال: 1979
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-66-1-13-24