Nonlinear monotone semigroups and viscosity solutions (Q5942605)

The author is interested in nonlinear semigroups \((S_t)_{t\geq 0}\) defined on some subspace \(X\subset C(\mathbb{R}^N)\) and satisfying the following monotonicity assumption: for any \(f,g\in X\) NEWLINE\[NEWLINEf\leq g\Rightarrow S_t(f)\leq S_t(g) \text{ for any }t\geq 0,NEWLINE\]NEWLINE where \(\leq\) denotes the partial ordering of \(C(\mathbb{R}^N)\) defined by NEWLINE\[NEWLINEf\leq g\Leftrightarrow f(x)\leq g(x)\text{ for all }x\in \mathbb{R}^N.NEWLINE\]NEWLINE He applies his results to viscosity solutions of a fully nonlinear, possibly degenerate, second-order parabolic pde.