Article
Keywords:
regularity; minimizers; non-polynomial growth
Summary:
Minimizers of a functional with exponential growth are shown to be smooth. The techniques developed for power growth are not applicable to the exponential case.
References:
                        
[1] Duc D.M., Eells J.: 
Regularity of exponentially harmonic functions. Intern. J. Math. 2 (1991), 395-408. 
MR 1113568 | 
Zbl 0751.58007[2] Gilbarg D., Trudinger N.S.: 
Elliptic Partial Differential Equations of Second Order. 2nd ed., Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1983. 
MR 0737190 | 
Zbl 1042.35002[3] Ladyzhenskaya O.A., Ural'tseva N.N.: 
Linear and Quasilinear Elliptic Equations. Izdat. Nauka, Moscow, 1964 (Russian). English translation: Academic Press, New York, 1968. 2nd Russian ed., 1973. 
MR 0244627 | 
Zbl 0177.37404[4] Lieberman G.M.: 
The conormal derivative problem for non-uniformly parabolic equations. Indiana Univ. Math. J. 37 (1988), 23-72. Addenda: ibid. 39 (1990), 279-281. 
Zbl 0707.35077[5] Lieberman G.M.: 
Gradient estimates for a class of elliptic systems. Ann. Mat. Pura Appl., to appear. 
MR 1243951 | 
Zbl 0819.35019[6] Serrin J.: 
Gradient estimates for solutions of nonlinear elliptic and parabolic equations. in: Contributions to Nonlinear Functional Analysis, Academic Press, New York, 1971, 565-601. 
MR 0402274 | 
Zbl 0271.35004[7] Simon L.M.: 
Interior gradient bounds for non-uniformly elliptic equations. Indiana Univ. Math. J. 25 (1976), 821-855. 
MR 0412605