On the removability of isolated singular points for elliptic equations involving variable exponent

Abstract

Abstract In this paper, we study the problem of removable isolated singularities for elliptic equations with variable exponents. We give a sufficient condition for removability of the isolated singular point for the equations in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>W</m:mi> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mi>p</m:mi> <m:mo>(</m:mo> <m:mi>x</m:mi> <m:mo>)</m:mo> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mi>Ω</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> ${W^{1,p(x)}(\Omega )}$ .