# Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of m-laplace equations

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In this paper we prove a boundary Harnack inequality for positive functions which vanish continuously on a portion of the boundary of a bounded domain-Î© R2 and which are solutions to a general equation of p-Laplace type, 1 < p < âˆž. We also establish the same type of result for solutions...

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We use moving planes and thin domain maximum principles to prove the maximum value of a positive solution to the equation Î”u + f(u) = 0 on a symmetric-convex domain Î© , with u = 0 on the boundary of Î© lies on the line of symmetry of the domain. If the domain has two or more lines of...