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1957), no. 43, 451-503. 10. 1. Bers and L. Nirenberg, On a representatIOn theorem for lmear elltpttc systems With dlscontmuous coeffictents and tts appitcatlOns, Convegno Internazionale sulle Equazioni aile Derivate Parziali, Cremonese, Roma, 1955, pp. 111-138. 11. L. Bers, F. John, and M. Schechter, Partwl Dtfferentlal Equations, Interscience Publishers, New York, 1964. 12. N. Meyers, An LP -estimate for the gradient of solutIOns of second order elliptiC dwergence form equatIOns, Ann. Sc. Norm.

Then, at = z(u) > R2. 5) . qo;. 2). Similarly, Rl ~ z(u). 2 follows from the strong maximum principle (cf. [12, Theorem 1]). 4. 1. Let 1 :::; m :::; n, and let 'if;(X) be a positIVe Cl-functlon In the annulus u E sn, p E [R l , R 2], 0 < Rl < R2 < a. Let z E C 3 (sn) be an admiSSible solutIOn of Eq. 6) satisfymg the mequalltles n: Rl :::; z(u) :::; R2, u E sn. F'/2(p)]:::; O. 4) Then where the constant C depends only on m, n, R 1 , R 2 , 'if;, and grad'if;. A Priori Estimates for Starshaped Hypersurfaces PROOF.

7]. 18 Giovanni Alessandrini and Vincenzo Nesi References 1. O. A. , Springer-Verlag, New York, 1985. 2. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic AnalYSIS for PerIOdic Structures, North-Holland, Amsterdam, 1978. 3. S. Spagnolo, Sui limite delle soluzlonl dl probleml dl Cauchy relativi all'equazlOne del calore, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (3) 21 (1967), 657-699. 4. ___ , Sulla convergenza di soluzlonl dl equazlOni paraboliche ed ellttttche, Ann. Sc. Norm. Super. Pisa, Cl.

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