Abstract
The inequality of Alexandrov, Bakel'man and Pucci is a basic tool in the theory of linear elliptic partial differential equations (PDEs) which are not in divergence form as well as in the more general theory of nonlinear elliptic PDEs. Here, in two dimensions, we prove the sharp form of the maximum principle as conjectured by Pucci in 1966, give sharp forms of removable singularity results and prove a number of results for the degenerate elliptic setting. These results make use of the substantial recent advances in the planar theory of quasiconformal mappings.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 49-74 |
| Number of pages | 26 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Issue number | 591 |
| DOIs | |
| State | Published - Feb 24 2006 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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Astala, K., Iwaniec, T., & Martin, G. (2006). Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane. Journal fur die Reine und Angewandte Mathematik, (591), 49-74. https://doi.org/10.1515/CRELLE.2006.014