22 citations · 35 across the 13 of their papers we have counts for
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math.AP2019
A Gagliardo-Nirenberg type inequality for rapidly decaying functions
Marek Fila, Johannes Lankeit
We improve the Gagliardo-Nirenberg inequality \[ \|φ\|_{L^q(\mathbb{R}^n)} \le C \|\nablaφ\|_{L^r(\mathbb{R}^n)} \mathcal{L}^{-(\frac 1q - \frac{n-r}{rn})} (\|\nablaφ\|_{L^r(\mathb…
math.AP2019
Lack of smoothing for bounded solutions of a semilinear parabolic equation
Marek Fila, Johannes Lankeit
We study a semilinear parabolic equation that possesses global bounded weak solutions whose gradient has a singularity in the interior of the domain for all . The singularity…
math.AP2019★ 2 cited
Continuation beyond interior gradient blow-up in a semilinear parabolic equation
Marek Fila, Johannes Lankeit
It is known that there is a class of semilinear parabolic equations for which interior gradient blow-up (in finite time) occurs for some solutions. We construct a continuation of s…