کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4592758 | 1335140 | 2008 | 75 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems](/preview/png/4592758.png)
We prove that Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half-space are well posed in L2 for small complex L∞ perturbations of a coefficient matrix which is either real symmetric, of block form or constant. All matrices are assumed to be independent of the transversal coordinate. We solve the Neumann, Dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order Dirac type operator. We establish quadratic estimates for this Dirac operator, which implies that the associated Hardy projection operators are bounded and depend continuously on the coefficient matrix. We also prove that certain transmission problems for k-forms are well posed for small perturbations of block matrices.
Journal: Journal of Functional Analysis - Volume 255, Issue 2, 15 July 2008, Pages 374-448