L2 estimates for commutators of the Dirichlet-to-Neumann Map associated to elliptic operators with complex-valued bounded measurable coefficients on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msubsup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo><mml:mn>1</mml:mn></mml…
نویسندگان
چکیده
In this paper we establish commutator estimates for the Dirichlet-to-Neumann Map associated to a divergence form elliptic operator in upper half-space R+n+1:={(x,t)∈Rn×(0,∞)}, with uniformly complex elliptic, L∞, t-independent coefficients. By standard pull-back mechanism, these results extend corresponding of Kenig, Lin and Shen Laplacian Lipschitz domain, which have application theory homogenization.
منابع مشابه
The Connections between Dirichlet, Regularity and Neumann Problems for Second Order Elliptic Operators with Complex Bounded Measurable Coefficients
The present paper discusses the relations between regularity, Dirichlet, and Neumann problems. Among other results, we prove that the solvability of the regularity problem does not imply the solvability of the dual Dirichlet problem for general elliptic operators with complex bounded measurable coefficients. This is strikingly different from the case of real operators, for which such an implica...
متن کاملThe Regularity Problem for Second Order Elliptic Operators with Complex-valued Bounded Measurable Coefficients
The present paper establishes a certain duality between the Dirichlet and Regularity problems for elliptic operators with t-independent complex bounded measurable coefficients (t being the transversal direction to the boundary). To be precise, we show that the Dirichlet boundary value problem is solvable in Lp ′ , subject to the square function and non-tangential maximal function estimates, if ...
متن کاملSubmajorization inequalities associated with $tau$-measurable operators
The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..
متن کاملSpectral Asymptotics for Dirichlet Elliptic Operators with Non-smooth Coefficients
We consider a 2m-th-order elliptic operator of divergence form in a domain of Rn, assuming that the coefficients are Hölder continuous of exponent r 2 (0, 1]. For the self-adjoint operator associated with the Dirichlet boundary condition we improve the asymptotic formula of the spectral function e( 2m , x , y) for x = y to obtain the remainder estimate O( n + dist(x , ) 1 n 1) with any 2 (0,...
متن کاملEstimates for Solutions to Non-uniformly Elliptic Pde’s with Measurable Coefficients
We propose to extend Talenti’s estimates on the L norm of the second order derivatives of the solutions of a uniformly elliptic PDE with measurable coefficients satisfying the Cordes condition to the non-uniformly elliptic case.
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 Mathematical Analysis and Applications
سال: 2021
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2021.125408