Analysis Seminar
主講者: | 1. 曾根 良夫教授 (中研院數學所, 京都大學), 2. Professor Eitan Tadmor (University of Maryland, USA) |
講題: | 1. Kinetic Equation Approach to Fluid-Dynamic Equations, 2. Linear equations in critical regularity spaces: Hierarchical construction of their nonlinear solutions |
時間: | 2010-12-13 (Mon.) 10:00 - 13:00 |
地點: | 數學所 722 研討室 (台大院區) |
Abstract: | 2. We construct uniformly bounded solutions of the equations div(U)=f and curl(U)=f, for general f’s in the critical regularity spaces L^d(R^d) and, respectively, L^3(R^3). The equations are linear but construction of their solutions is not. Our constructions are special cases of a general framework for solving linear equations, L(U)=f, covered by the closed range theorem. The solutions are realized in terms of nonlinear hierarchical representations, U=sum(u_j), which we introduced earlier in the context of image processing. The u_j's are constructed recursively as proper minimizers, yielding a multi-scale decomposition of the solutions U. |
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