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Flattening results for elliptic PDEs in unbounded domains with applications to overdetermined problems. (English) Zbl 1236.35058

Summary: 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.

MSC:

35J61 Semilinear elliptic equations
35N99 Overdetermined problems for partial differential equations and systems of partial differential equations
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