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The Regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients
| Content Provider | CiteSeerX |
|---|---|
| Author | Hofmann, Steve Kenig, Carlos Mayboroda, Svitlana Pipher, Jill |
| Abstract | Abstract. The present paper establishes a certain duality between the Dirich-let and Regularity problems for elliptic operators with t-independent complex bounded measurable coefficients (t being the transversal direction to the bound-ary). To be precise, we show that the Dirichlet boundary value problem is solv-able in Lp, subject to the square function and non-tangential maximal function estimates, if and only if the corresponding Regularity problem is solvable in Lp. Moreover, the solutions admit layer potential representations. In particular, we prove that for any elliptic operator with t-independent real (possibly non-symmetric) coefficients there exists a p> 1 such that the Regular-ity problem is well-posed in Lp. 1. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Measurable Coefficient Regularity Problem Second Order Elliptic Operator Elliptic Operator Non-tangential Maximal Function Estimate Regular-ity Problem T-independent Complex Transversal Direction Corresponding Regularity Problem Certain Duality Layer Potential Representation Square Function Dirichlet Boundary Value Problem |
| Content Type | Text |
| Resource Type | Article |
