The Maximum Principle for Equations with Composite Coefficients
dc.contributor.author | Lieberman, Gary M. | |
dc.date.accessioned | 2019-12-20T21:10:31Z | |
dc.date.available | 2019-12-20T21:10:31Z | |
dc.date.issued | 2000-05-22 | |
dc.description.abstract | It 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.department | Mathematics | |
dc.format | Text | |
dc.format.extent | 17 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.identifier.citation | Lieberman, G. M. (2000). The maximum principle for equations with composite coefficients. Electronic Journal of Differential Equations, 2000(38), pp. 1-17. | |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | https://hdl.handle.net/10877/9128 | |
dc.language.iso | en | |
dc.publisher | Southwest Texas State University, Department of Mathematics | |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.source | Electronic Journal of Differential Equations, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
dc.subject | Elliptic differential equations | |
dc.subject | Oblique boundary conditions | |
dc.subject | Maximum principles | |
dc.subject | Holder estimates | |
dc.subject | Harnack inequality | |
dc.subject | Parabolic differential equations | |
dc.title | The Maximum Principle for Equations with Composite Coefficients | |
dc.type | Article |