We study the minimizer $u$ of a convex functional in the plane which is not G\^ateaux-differentiable. Namely, we show that the set of critical points of any $C\sp1$-smooth minimizer can not have isolated points. Also, by means of some appropriate approximating scheme and viscosity solutions, we determine an Euler-Lagrange equation that $u$ must satisfy. By applying the same approximating scheme, we can pair $u$ with a function $v$ which may be regarded as the stream function of $u$ in a suitable generalized sense.

Critical points of solutions of degenerate elliptic equations in the plane / S. Cecchini; R. Magnanini. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 39:(2010), pp. 121-138. [10.1007/s00526-009-0304-8]

Critical points of solutions of degenerate elliptic equations in the plane

MAGNANINI, ROLANDO
2010

Abstract

We study the minimizer $u$ of a convex functional in the plane which is not G\^ateaux-differentiable. Namely, we show that the set of critical points of any $C\sp1$-smooth minimizer can not have isolated points. Also, by means of some appropriate approximating scheme and viscosity solutions, we determine an Euler-Lagrange equation that $u$ must satisfy. By applying the same approximating scheme, we can pair $u$ with a function $v$ which may be regarded as the stream function of $u$ in a suitable generalized sense.
39
121
138
S. Cecchini; R. Magnanini
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/366845
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