Abstract
We show that every weak supersolution of a variable exponent -Laplace equation is lower semicontinuous and that the singular set of such a function is of zero capacity if the exponent is logarithmically Holder continuous. As a technical tool we derive Harnack-type estimates for possibly unbounded supersolutions.
Highlights
The purpose of this work is to study regularity theory related to partial differential equations with nonstandard growth conditions
An interesting feature of this theory is that estimates are intrinsic in the sense that they depend on the solution itself
Using Harnack-type estimates we show that every supersolution has a lower semicontinuous representative
Summary
We show that every weak supersolution of a variable exponent p-Laplace equation is lower semicontinuous and that the singular set of such a function is of zero capacity if the exponent is logarithmically Holder continuous. As a technical tool we derive Harnacktype estimates for possibly unbounded supersolutions
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