Semilinear elliptic PDEs are dealt with, either in the half-space or in overdetermined settings. We obtain several new results and also give new proofs of celebrated theorems by exploiting some geometric analysis of level sets, a geometric inequality and a pointwise gradient estimate.
Flattening results for elliptic PDEs in unbounded domains with applications to overdetermined problems / A. Farina, E. Valdinoci. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 195:3(2010 Mar), pp. 1025-1058. [10.1007/s00205-009-0227-8]
Flattening results for elliptic PDEs in unbounded domains with applications to overdetermined problems
E. ValdinociUltimo
2010
Abstract
Semilinear elliptic PDEs are dealt with, either in the half-space or in overdetermined settings. We obtain several new results and also give new proofs of celebrated theorems by exploiting some geometric analysis of level sets, a geometric inequality and a pointwise gradient estimate.
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