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Symmetry via antisymmetric maximum principles in nonlocal problems of variable order.(English)Zbl 1346.35010

The authors study nonlinear problems of the type \(Iu=f(x,u)\) in \(\Omega\), \(u=0\) on \(\mathbb R^N\setminus\Omega\), for open bounded \(\Omega\). Here \(I\) is nonlocal, e.g. a fractional Laplacian, and of varying order. Under structural assumptions on \(I\), \(\Omega\) and \(f\) with respect to a fixed direction \(\xi\) they prove Steiner symmetry of solutions with a new variant of the maximum principle.

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35B50 Maximum principles in context of PDEs
35R11 Fractional partial differential equations

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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