Abstract
We determine a class of Carathéodory functions G for which the minimum formulated in the problem (1.1) below is achieved at a Schwarz symmetric function satisfying the constraint. Our hypotheses about G seem natural and, as our examples show, they are optimal from some points of view.
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Hajaiej, H., Stuart, C. Existence and non-existence of Schwarz symmetric ground states for elliptic eigenvalue problems. Annali di Matematica 184, 297–314 (2005). https://doi.org/10.1007/s10231-004-0114-8
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DOI: https://doi.org/10.1007/s10231-004-0114-8