A Harnack inequality for nonlinear equations

Author:
James Serrin

Journal:
Bull. Amer. Math. Soc. **69** (1963), 481-486

DOI:
https://doi.org/10.1090/S0002-9904-1963-10971-4

MathSciNet review:
0150443

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References | Additional Information

**1.**D. Gilbarg,*Some local properties of elliptic equations*, Proc. Sympos. Pure Math., Vol. 4, Partial Differential Equations, pp. 127-142, Amer. Math. Soc., Providence, R. I., 1961. MR**133578****2.**D. Gilbarg,*Boundary value problems for non-linear elliptic equations*, Nonlinear Problems (edited by R. E. Langer), pp. 151-160, Univ. of Wisconsin Press, Madison, Wis., 1963. MR**146506****3.**D. Gilbarg and J. Serrin,*On isolated singularities of solutions of second order elliptic differential equations*, J. Analyse Math. 4 (1955-56), 309-340. MR**81416****4.**O. A. Ladyzhenskaya and N. Uraltseva,*Quasi-linear elliptic equations and variational problems with many independent variables*, Uspehi Mat. Nauk 16 (1961), 19-92; translated in Russian Math. Surveys 16 (1961), 17-91.**5.**W. Littman, G. Stampacchia and H. Weinberger,*Regular points for elliptic equations with discontinuous coefficients*(to appear). MR**161019****6.**C. B. Morrey, Jr.,*Second order elliptic equations and Hölder continuity*, Math. Z. 72 (1959), 146-164. MR**120446****7.**C. B. Morrey, Jr.,*Existence and differentiability theorems for variational problems for multiple integrals*, Partial Differential Equations and Continuum Mechanics, pp. 241-270, Univ. of Wisconsin Press, Madison, Wis., 1961. MR**121690****8.**J. Moser,*On Harnack's theorem for elliptic differential equations*, Comm. Pure Appl. Math. 14 (1961), 577-591. MR**159138****9.**H. Royden,*The growth of a fundamental solution of an elliptic divergence structure equation*, Studies in Mathematical Analysis and Related Topics: Essays in honor of G. Pólya, pp. 333-340, Stanford Univ. Press, Stanford, Calif., 1962. MR**145190****10.**J. Serrin,*Dirichlet's principle in the calculus of variations*, Proc. Sympos. Pure Math., Vol. 4, Partial Differential Equations, pp. 17-22, Amer. Math. Soc., Providence, R. I., 1961. MR**137012**

Additional Information

DOI:
https://doi.org/10.1090/S0002-9904-1963-10971-4