The Maximum Principle for Equations with Composite Coefficients

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dc.contributor.authorLieberman, Gary M.
dc.date.accessioned2019-12-20T21:10:31Z
dc.date.available2019-12-20T21:10:31Z
dc.date.issued2000-05-22
dc.description.abstractIt is well-known that the maximum of the solution of a linear elliptic equation can be estimated in terms of the boundary data provided the coefficient of the gradient term is either integrable to an appropriate power or blows up like a small negative power of distance to the boundary. Apushkinskaya and Nazarov showed that a similar estimate holds if this term is a sum of such functions provided the boundary of the domain is sufficiently smooth and a Dirichlet condition is prescribed. We relax the smoothness of the boundary and also consider non-Dirichlet boundary conditions using a variant of the method of Apushkinskaya and Nazarov. In addition, we prove a Holder estimate for solutions of oblique derivative problems for nonlinear equations satisfying similar conditions.
dc.description.departmentMathematics
dc.formatText
dc.format.extent17 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationLieberman, G. M. (2000). The maximum principle for equations with composite coefficients. <i>Electronic Journal of Differential Equations, 2000</i>(38), pp. 1-17.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/9128
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectElliptic differential equations
dc.subjectOblique boundary conditions
dc.subjectMaximum principles
dc.subjectHolder estimates
dc.subjectHarnack inequality
dc.subjectParabolic differential equations
dc.titleThe Maximum Principle for Equations with Composite Coefficients
dc.typeArticle

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