Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth
<p/> <p>We show that every weak supersolution of a variable exponent <inline-formula><graphic file="1687-2770-2007-048348-i1.gif"/></inline-formula>-Laplace equation is lower semicontinuous and that the singular set of such a function is of zero capacity if th...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
SpringerOpen
2007-01-01
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Series: | Boundary Value Problems |
Online Access: | http://www.boundaryvalueproblems.com/content/2007/048348 |
Summary: | <p/> <p>We show that every weak supersolution of a variable exponent <inline-formula><graphic file="1687-2770-2007-048348-i1.gif"/></inline-formula>-Laplace equation is lower semicontinuous and that the singular set of such a function is of zero capacity if the exponent is logarithmically Hölder continuous. As a technical tool we derive Harnack-type estimates for possibly unbounded supersolutions.</p> |
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ISSN: | 1687-2762 1687-2770 |