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A new proof of local \(C^{1,\alpha}\) regularity for solutions of certain degenerate elliptic P.D.E. (English) Zbl 0508.35036


MSC:

35J70 Degenerate elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35J20 Variational methods for second-order elliptic equations
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References:

[1] Almoren, F.J, Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularily structure, Ann. of math., 87, 327-391, (1968)
[2] Gilbarg, D; Trudinger, N.S, Elliptic partial differential equations of second order, (1977), Springer-Verlag New York · Zbl 0691.35001
[3] Lady┼żenskaja, O.A; Ural’ceva, N.N, Linear and quasilinear elliptic equations, (1968), Academic Press New York
[4] Lewis, J.L, Capacitary functions in convex rings, Arch. rational mech. anal., 66, 201-224, (1977) · Zbl 0393.46028
[5] Moser, J, A new proof of Degiorgi’s theorem concerning the regularity problem for elliptic differential equations, Comm. pure appl. math., 13, 457-468, (1960) · Zbl 0111.09301
[6] Uhlenbeck, K, Regularity for a class of nonlinear elliptic systems, Acta math., 138, 219-240, (1977) · Zbl 0372.35030
[7] Ural’ceva, N.N, Degenerate quasilinear elliptic systems, (), 184-222, [in Russian]
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