TY - JOUR
T1 - Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane
AU - Astala, K.
AU - Iwaniec, T.
AU - Martin, G.
N1 - Funding Information:
Astala was supported in part by the Academy of Finland, projects 34082 and 41933, Iwaniec by the National Science Foundation grants DMS-0301582 and DMS-0244297, Martin by the N.Z. Marsden Fund and the N.Z. Royal Society (James Cook Fellowship).
PY - 2006/2/24
Y1 - 2006/2/24
N2 - 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.
AB - 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.
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U2 - 10.1515/CRELLE.2006.014
DO - 10.1515/CRELLE.2006.014
M3 - Article
AN - SCOPUS:33646703092
SP - 49
EP - 74
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 591
ER -