The Inhomogeneous Dirichlet Problem forΔ2in Lipschitz Domains
نویسندگان
چکیده
منابع مشابه
The L Dirichlet Problem for the Stokes System on Lipschitz Domains
We study the Lp Dirichlet problem for the Stokes system on Lipschitz domains. For any fixed p > 2, we show that a reverse Hölder condition with exponent p is sufficient for the solvability of the Dirichlet problem with boundary data in LpN (∂Ω, R d). Then we obtain a much simpler condition which implies the reverse Hölder condition. Finally, we establish the solvability of the Lp Dirichlet prob...
متن کاملNecessary and Sufficient Conditions for the Solvability of the L Dirichlet Problem on Lipschitz Domains
We study the homogeneous elliptic systems of order 2l with real constant coefficients on Lipschitz domains in R, n ≥ 4. For any fixed p > 2, we show that a reverse Hölder condition with exponent p is necessary and sufficient for the solvability of the Dirichlet problem with boundary data in L. We also obtain a simple sufficient condition. As a consequence, we establish the solvability of the L ...
متن کاملNecessary and sufficient conditions for the solvability of the Lp Dirichlet problem on Lipschitz domains
We study the homogeneous elliptic systems of order 2 with real constant coefficients on Lipschitz domains in Rn, n ≥ 4. For any fixed p > 2, we show that a reverse Hölder condition with exponent p is necessary and sufficient for the solvability of the Dirichlet problem with boundary data in Lp. We also obtain a simple sufficient condition. As a consequence, we establish the solvability of the L...
متن کاملRegularity Problem on Lipschitz Domains
This paper contains two results on the Lp regularity problem on Lipschitz domains. For second order elliptic systems and 1 < p < ∞, we prove that the solvability of the Lp regularity problem is equivalent to that of the Lp ′ Dirichlet problem. For higher order elliptic equations and systems, we show that if p > 2, the solvability of the Lp regularity problem is equivalent to a weak reverse Höld...
متن کاملThe Neumann Problem on Lipschitz Domains
Au — 0 in D; u = ƒ on bD9 where ƒ and its gradient on 3D belong to L(do). For C domains, these estimates were obtained by A. P. Calderón et al. [1]. For dimension 2, see (d) below. In [4] and [5] we found an elementary integral formula (7) and used it to prove a theorem of Dahlberg (Theorem 1) on Lipschitz domains. Unknown to us, this formula had already been discovered long ago by Payne and We...
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: Journal of Functional Analysis
سال: 1998
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3300