By B. D. Coleman (auth.), Giuseppe Grioli (eds.)
Lectures: B. Coleman: On international and native sorts of the second one legislation of thermodynamics.- J. Serrin: comparability and averaging equipment in mathematical physics.- H. Ziegler: Thermodynamic facets of continuum mechanics.- Seminars: C. Agostinelli: I. Un teorema di media sul flusso di energia nel moto di un fluido di alta conduttivit� elettrica in cui si genera un campo magnetico. II. Su alcuni teoremi di media in magnetofluidodinamica nel caso stazionario.- D. Graffi: I. Principi di minimo e variazionali nel campo elettromagnetico. II. Teoremi di reciprocit� nei fenomeni non stazionari.- G. Grioli: I. Propriet� generali di media nella meccanica dei continui e loro applicazioni. II. Problemi di integrazione nella teoria dell´equilibrio elastico.
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Sample text
Its conclusion is somewhat weaker than Nirenberg's but this is compensated for by the greater generality allowed the differential operator ~u , which may in particular be strongly nonlinear. 57 -14J. Serrin References: Chapter I •• •• E. Hopf, Elementare Bemerkungen uber die Losungen Partieller Differentialgleichungen Zweiter Ondnung vom Elliptischen Typus. Sitz. Preuss. Akad. Wiss . £ (1927), 147-152. E. Hopf, A remark on linear elliptic equations of second order. Proc. Amer. Math. Soc. ~ (1952), 791-793.
1 J and 1 a ij ) i 2,2 ~j = c ~ 52 -'~2 - (v. t) ~(c 2 2~2 - q ) 5 . - 9J. Serrin Therefore, if the flow is subsonic (q < c) then the equation is elliptic and the maximum principle applies. Since a similar equation holds for the stream function in plane flow, we have thus proved Theorem 4. Now differentiate the velocity potential equation with respect to x. It is not difficult to see (cf. [3J or (6J) that the result is an equation of the form a .. lJ ~u + linear terms in ? J =0 f) x. 1 Th'ls the velocity components u, v, w, also satisfy the maximum principle, and Theorem 5 is proved.
3 (1954). 303-314. [1 ~A. Friedman. Free boundary problems for parabolic equations 1. II, ·~ber III. Journ. Math. Mech. 8 (1959). 499-517; 9 (1960). 19-66. 327-346. (l~R. Redheffer. Bemerkungen Monotonie und Fehlerabsch'~tzung bei nichtlinearen partiellen Differentialgleichungen. Arch. Rat. Mech. Anal. - 10 (1962). 427-457. Maximum Principles and Comparison Methods for Other Types of Equation,; l1~S. Agmon. L. Nirenberg. and M. Protter. Comm. Pure Appl. Math. ~ (195:l), 445. 59 - 16 J. Serrin Q6)C.
