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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{ZNSL_1999_259_a7,
     author = {A. I. Nazarov},
     title = {About {\textquotedblleft}one-dimensionality{\textquotedblright} of the extremal in the {Poincare} inequality in the square},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {167--181},
     year = {1999},
     volume = {259},
     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/