论文标题
边界价值问题和具有块结构的椭圆系统的耐铁空间
Boundary value problems and Hardy spaces for elliptic systems with block structure
论文作者
论文摘要
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents.在这项工作之前，只有二维情况才被完全理解。在较高的维度中，已经建立了较小的指数范围和此类系统子类的部分结果。提出的独特结果是全新的。我们还阐明了针对分数规律性数据问题的最佳范围。方法在过去的二十年中使用和改进的方法有一些新的结果，用于研究此类问题：Kato Square root估计和Riesz变换，与操作员相关的耐寒空间，非二元估计，非区域性估计和方形功能和抽象层势能，以替代当地正常解决方案的基本解决方案，以替代基本解决方案。这本独立的专着提供了有关该领域的全面概述，并统一了许多通过多种方法获得的早期结果。
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established. The presented uniqueness results are completely new. We also elucidate optimal ranges for problems with fractional regularity data. Methods use and improve, with some new results, all the machinery developed over the last two decades to study such problems: the Kato square root estimates and Riesz transforms, Hardy spaces associated to operators, off-diagonal estimates, non-tangential estimates and square functions and abstract layer potentials to replace fundamental solutions in the absence of local regularity of solutions. This self-contained monograph provides a comprehensive overview on the field and unifies many earlier results that have been obtained by a variety of methods.
