A Strong Maximum Principle for some quasilinear elliptic equations |
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Authors: | J L Vázquez |
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Institution: | (1) División de Matemáticas, Universidad Autónoma, Madrid-34, Spain |
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Abstract: | In its simplest form the Strong Maximum Principle says that a nonnegative superharmonic continuous function in a domain
n
,n 1, is in fact positive everywhere. Here we prove that the same conclusion is true for the weak solutions of – u + (u) = f with a nondecreasing function ,(0)=0, andf0 a.e. in if and only if the integral((s)s)
–1/2
ds diverges ats=0+. We extend the result to more general equations, in particular to –
p
u + (u) =f where
p
(u) = div(|Du|
p-2
Du), 1 <p < . Our main result characterizes the nonexistence of a dead core in some reaction-diffusion systems.This work was partly done while the author was visiting the University of Minnesota as a Fulbright Scholar. |
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Keywords: | |
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