5 papers · 1 filter
Oscillatory blow-up and gradient estimates for semilinear heat equations
Pavol Quittner, Philippe Souplet
For reaction-diffusion with blow-up nonlinearities, we consider the question whether the sup norm of any positive blow-up solution must be eventually monotone nondecreasing in time…
Threshold, subthreshold and global unbounded solutions of superlinear heat equations
Pavol Quittner, Philippe Souplet
We consider the semilinear heat equation with a superlinear nonlinearity and we study the properties of threshold or subthreshold solutions, lying on or below the boundary between…
Elliptic regularity estimates with optimized constants and applications
Boyan Sirakov, Philippe Souplet
We revisit the classical theory of linear second-order uniformly elliptic equations in divergence form whose solutions have Hölder continuous gradients, and prove versions of the…
Liouville theorems and universal estimates for superlinear parabolic problems without scale invariance
Pavol Quittner, Philippe Souplet
We establish Liouville type theorems in the whole space and in a half-space for parabolic problems without scale invariance. To this end, we employ two methods, respectively based…
Liouville theorems and universal estimates for superlinear elliptic problems without scale invariance
Pavol Quittner, Philippe Souplet
We give applications of known and new Liouville type theorems to universal singularity and decay estimates for non scale invariant elliptic problems, including Lane-Emden and SchrÃ…