Geodesic
About ``one-dimensionality'' of the extremal in the Poincare inequality in the square
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 167-181

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Conditions of local extremality and nonextremality of “one-dimensional” functions for the functional induced by Poincaré inequality in the square and in the rectangle are obtained. 
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     author = {A. I. Nazarov},
     title = {About ``one-dimensionality'' of the extremal in the {Poincare} inequality in the square},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {167--181},
     publisher = {mathdoc},
     volume = {259},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a7/}
}
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A. I. Nazarov. About ``one-dimensionality'' of the extremal in the Poincare inequality in the square. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 167-181. http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a7/