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The strong maximum principle revisited by Pucci P., Serrin J.

By Pucci P., Serrin J.

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Stakgold, The formation of the dead core in parabolic reaction–diffusion problems, Trans. Amer. Math. , 286 (1984), 275–293. [2] Bardi, M. and F. Da Lio, On the strong maximum principle for fully nonlinear degenerate elliptic equations, Arch. , 73 (2000), 276–285. , G. I. Diaz, Uniqueness and continuum of foliated solutions for a quasilinear elliptic equation with a nonlipschitz nonlinearity, Comm. Partial Diff. Equations, 17 (1992), 1037–1050. , H. Brezis and M. Crandall, A semilinear equation in L1 (Rn ), Ann.

1). 2) reduces just to the manifold Laplacian, see [43], page 232. A specific example is given by the variational integral 1 √ |∇u|pg + F (u) dM, p > 1, where dM = gdx on Ω, Ω p √ introduced by Mossino ([24], page 40), though without the volume factor g. Here of course A(ρ) = ρp−2 , p > 1. Other examples are given also in [25]. 13) when aij (x, u) = g(x)g ij (x), B(x, u, ξ) = g(x)f (u). 13). As at the beginning of the section, we assume that (A1) and (A2) are valid, and additionally that the tensors [g ij ] = [g ij (x, u)] and [aij ] = [aij (x, u)] are continuously differentiable, 36 P.

Ramaswamy, A strong maximum principle for a class of non– positone singular elliptic problems, to appear in Nonlinear Diff. Eqs. Appl.. , Nonlinear Partial Differential Equations and Free Boundaries, Pitman Research Notes in Mathematics, 106, 1985. , Some properties of solutions of degenerate second order PDE in non divergence form, Appl. , 20 (1985), 309–336. I. A. Herrero, Estimates on the support of the solutions of some nonlinear elliptic and a parabolic problems, Proc. Royal Soc. Edinburgh, 89-A (1981), 249–258.

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