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Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth

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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 Hölder continuous. As a technical tool we derive Harnack-type estimates for possibly unbounded supersolutions.



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Correspondence to Petteri Harjulehto.

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Harjulehto, P., Kinnunen, J. & Lukkari, T. Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth. Bound Value Probl 2007, 048348 (2006) doi:10.1155/2007/48348

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  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Nonlinear Equation