Critical points of solutions of degenerate elliptic equations in the plane |
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| Authors: | Simone Cecchini Rolando Magnanini |
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| Institution: | 1. Dipartimento di Matematica U. Dini, Università di Firenze, viale Morgagni 67/A, 50134, Firenze, Italy
2. Dipartimento di Scienze e Metodi dell’Ingegneria, Università degli Studi di Modena e Reggio Emilia, via G. Amendola, 2 - Pad. Morselli, 42100, Reggio Emilia, Italy
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| Abstract: | We study the minimizer u of a convex functional in the plane which is not Gâteaux-differentiable. Namely, we show that the set of critical points of any C 1-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. |
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