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math.AP2024
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 g…
math.AP2024
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…
math.AP2024
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 Schrö…