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Global estimates of Hölder continuity for a class of divergente-form elliptic equations. (English) Zbl 0295.35027


MSC:

35J25 Boundary value problems for second-order elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35J60 Nonlinear elliptic equations
35J67 Boundary values of solutions to elliptic equations and elliptic systems
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[2] Giusti, E, Boundary behaviour of non-parametric minimal surfaces. Indiana University Math. Journal 22 (1972). · Zbl 0262.35020
[3] Ladyzhenskaya, O. A. & N. N. Ural’tseva, Local estimates for gradients of solutions of non-uniformly elliptic and parabolic equations Part II, pp. 687-703. Comm. Pure and Appl. Math. 23 (1970). · Zbl 0193.07202
[4] Michael, J. H. & L. M. Simon, Sobolev and mean-value inequalities on generalised submanifolds of ? n . Comm. Pure and Appl. Math. 26 (1973). · Zbl 0256.53006
[5] Moser, J., A new proof of DeGiorgi’s theorem concerning the regularity problem for elliptic differential equations. Comm. Pure and Appl. Math. 13 (1960). · Zbl 0111.09301
[6] Trudinger, N. S., A new proof of the interior gradient bound for the minimal surface equation in n-dimensions. Proc. Nat. Acad. Sci. USA 69 (1972). · Zbl 0231.53007
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