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Harmonic analysis techniques for second order elliptic boundary value problems: dedicated to the memory of Professor Antoni Zygmund. (English) Zbl 0812.35001
Regional Conference Series in Mathematics. 83. Providence, RI: American Mathematical Society (AMS). xii, 146 p. (1994).
Publisher’s description: In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for applications, and they have turned out to have profound and fascinating connections with many areas of analysis. Techniques from harmonic analysis have proved to be extremely useful in these studies, both as concrete tools in establishing theorems and as models which suggest what kind of result might be true. Kenig describes these developments and connections for the study of classical boundary value problems on Lipschitz domains and for the corresponding problems for second order elliptic equations in divergence form. He also points out many interesting problems in this area which remain open.

MSC:
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
35J25 Boundary value problems for second-order elliptic equations
Biographic References:
Zygmund, Antoni
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