Removable sets for subcaloric functions and solutions of semilinear heat equations with absorption (Q297516)

Let \(u\) be a subcaloric function in \(\Omega \setminus E\), where \(\Omega \) is open and \(E\) is a relatively closed subset of \(\Omega \). Under certain conditions on the upper Minkowski content of \(E\) and growth of \(u\) in a neighbourhood of \(E\) it is shown that \(u\) has a subcaloric extension to \(\Omega \). Under the same conditions it is shown that \(E\) is a removable set for caloric functions and that, if \(u\) is a nonnegative \(C^{2,1}\)-solution of \(\Delta u-\partial_t u=u^q\) in \(\Omega \setminus E\), then \(u\) can be extended to the whole \(\Omega \) as a \(C^{2,1}\)-solution of this equation in \(\Omega \).