In a space of dimensions m, with m greater or equal to 2, a radial variational problem related to a priori estimates for solutions to extremal elliptic equations with fixed ellipticity constant is investigated. The problem is solved in Lp spaces, with p>m, for ellipticity constant values in a proper interval and a representation of maximizing function is explicitly determined. Otherwise, this fact is no longer true.
On a variational problem for radial solutions to extremal elliptic equations / O. Arena; P. Buonocore. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 1618-1891. - STAMPA. - 188:(2009), pp. 187-206. [10.1007/s10231-008-0071-8]
On a variational problem for radial solutions to extremal elliptic equations
ARENA, ORAZIO;
2009
Abstract
In a space of dimensions m, with m greater or equal to 2, a radial variational problem related to a priori estimates for solutions to extremal elliptic equations with fixed ellipticity constant is investigated. The problem is solved in Lp spaces, with p>m, for ellipticity constant values in a proper interval and a representation of maximizing function is explicitly determined. Otherwise, this fact is no longer true.
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