On functions, whose lines of steepest descent bend proportionally to level lines
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 10 (1983) no. 4, p. 587-605 
@article{ASNSP_1983_4_10_4_587_0,
     author = {Talenti, Giorgio},
     title = {On functions, whose lines of steepest descent bend proportionally to level lines},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 10},
     number = {4},
     year = {1983},
     pages = {587-605},
     zbl = {0542.35007},
     mrnumber = {753157},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1983_4_10_4_587_0}
}

Talenti, Giorgio. On functions, whose lines of steepest descent bend proportionally to level lines. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 10 (1983) no. 4, pp. 587-605. http://www.numdam.org/item/ASNSP_1983_4_10_4_587_0/

[1] R. Courant - D. Hilbert, Methods of mathematical physics, Interscience, 1962.

[2] H. Federer, Geometric measure theory, Springer-Verlag, 1969. | MR 257325 | Zbl 0176.00801

[3] M. Longinetti, Sulla convessità delle linee di livello di funzioni armoniche, Boll. Un. Mat. It., ser. 6, vol. 2-A (1983), pp. 71-75. | Zbl 0525.35013

[4] F. John, Partial differential equations, Springer-Verlag, 1971. | MR 304828 | Zbl 0209.40001

[5] F. John, Formation of singularities in one-dimensional wave propagation, Comm. Pure Appl. Math., 27 (1974), pp. 377-405. | MR 369934 | Zbl 0302.35064

[6] S. Klainerman - A. Majda, Formation of singularities for wave equation including the nonlinear vibrating string, Comm. Pure Appl. Math., 33 (1980), pp. 241-263. | MR 562736 | Zbl 0443.35040

[7] P.D. Lax, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys., 5 (1964), pp. 611-613. | MR 165243 | Zbl 0135.15101

[8] S.A. Levin, Nonlinear boundary problems for a quasilinear parabolic equation, J. Diff. Eq., 5 (1969), pp. 32-37. | MR 233085 | Zbl 0169.13003

[9] G. Talenti, A note on the Gauss curvature of harmonic and minimal surfaces, Pacific J. Math., 101 (1982), pp. 477-492. | MR 675412 | Zbl 0496.53004