Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s | ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV)

Free Access

Issue		ESAIM: COCV Volume 19, Number 2, April-June 2013


Page(s)		616 - 627
DOI		https://doi.org/10.1051/cocv/2012024
Published online		14 March 2013

S. Bernstein, Über ein geometrisches theorem und seine anwendung auf die partiellen differentialgleichungen vom elliptischen Typus. Math. Z. 26 (1927) 551–558. [CrossRef] [MathSciNet] [Google Scholar]
L. Caffarelli, N. Garofalo and F. Segala, A gradient bound for entire solutions of quasi-linear equations and its consequences. Commun. Pure Appl. Math. 47 (1994) 1457–1473. [CrossRef] [Google Scholar]
D. Castellaneta, A. Farina and E. Valdinoci, A pointwise gradient estimate for solutions of singular and degenerate PDEs in possibly unbounded domains with nonnegative mean curvature. Commun. Pure Appl. Anal. 11 (2012) 1983–2003. [CrossRef] [MathSciNet] [Google Scholar]
D.G. De Figueiredo and P. Ubilla, Superlinear systems of second-order ODE’s. Nonlinear Anal. 68 (2008) 1765–1773. [CrossRef] [MathSciNet] [Google Scholar]
D.G. De Figueiredo, J. Sánchez and P. Ubilla, Quasilinear equations with dependence on the gradient. Nonlinear Anal. 71 (2009) 4862–4868. [CrossRef] [MathSciNet] [Google Scholar]
E. DiBenedetto, C^{1 + α} local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 7 (1983) 827–850. [CrossRef] [MathSciNet] [Google Scholar]
A. Farina, Liouville-type theorems for elliptic problems, in Handbook of differential equations: stationary partial differential equations, Elsevier/North-Holland, Amsterdam. Handb. Differ. Equ. 4 (2007) 61–116. [Google Scholar]
A. Farina and E. Valdinoci, Flattening results for elliptic PDEs in unbounded domains with applications to overdetermined problems. Arch. Ration. Mech. Anal. 195 (2010) 1025–1058. [CrossRef] [MathSciNet] [Google Scholar]
A. Farina and E. Valdinoci, A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature. Adv. Math. 225 (2010) 2808–2827. [CrossRef] [MathSciNet] [Google Scholar]
A. Farina and E. Valdinoci, A pointwise gradient bound for elliptic equations on compact manifolds with nonnegative Ricci curvature. Discrete Contin. Dyn. Syst. 30 (2011) 1139–1144. [CrossRef] [MathSciNet] [Google Scholar]
D. Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, Berlin (2001). Reprint of the 1998 edition. [Google Scholar]
P. Hartman, Ordinary differential equations, Society for Industrial and Applied Mathematics SIAM, Philadelphia, PA. Classics Appl. Math. 38 (2002). Corrected reprint of the second (1982) edition [Birkhäuser, Boston, MA, MR0658490 (83e:34002)]. With a foreword by Peter Bates. [Google Scholar]
L. Modica, A gradient bound and a Liouville theorem for nonlinear Poisson equations. Commun. Pure Appl. Math. 38 (1985) 679–684. [CrossRef] [Google Scholar]
L.E. Payne, Some remarks on maximum principles. J. Anal. Math. 30 (1976) 421–433. [CrossRef] [Google Scholar]
J. Serrin, Entire solutions of nonlinear Poisson equations. Proc. London Math. Soc. 24 (1972) 348–366. [CrossRef] [MathSciNet] [Google Scholar]
R.P. Sperb, Maximum principles and their applications, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York. Math. Sci. Eng. 157 (1981). [Google Scholar]
P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations. J. Differ. Equ. 51 (1984) 126–150. [CrossRef] [MathSciNet] [Google Scholar]

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