Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth
Copyright policy )Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth
In this paper, possibly unbounded supersolutions of a variable exponent \(p\)-Laplace equation are studied. Using the Moser iteration scheme, a Harnack-type inequality is obtained in which \(L^\infty\)-estimates are replaced with certain \(L^p\)-estimates for small values of \(p\). This permits to show that every supersolution has a lower semi-continuous representative. Finally, the main result of this paper states that the singular set of a supersolution is of zero capacity if the exponent is logarithmically Hölder continuous.
- University of Helsinki Finland
- Oulu University Hospital Finland
- Helsinki University of Technology Finland
- University of Oulu Finland
QA299.6-433, Regularity of generalized solutions of PDE, Variational methods for second-order elliptic equations, supersolutions, Harnack inequality, Algebra and Number Theory, variable exponent, Nonlinear elliptic equations, Analysis, \(p\)-Laplace equation
QA299.6-433, Regularity of generalized solutions of PDE, Variational methods for second-order elliptic equations, supersolutions, Harnack inequality, Algebra and Number Theory, variable exponent, Nonlinear elliptic equations, Analysis, \(p\)-Laplace equation
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