Biharmonic nonlinear scalar field equations

Mederski, Jarosław; Siemianowski, Jakub

doi:10.5445/IR/1000135513

Biharmonic nonlinear scalar field equations

Mederski, Jarosław; Siemianowski, Jakub

Abstract:

We prove a Brezis-Kato-type regularity result for weak solutions to the biharmonic nonlinear
equation

Δ^{2} u = g (x, u) in R^{N}

with a Carathéodory function

g : R^{N} \times R \to R

N \geq 5

. The regularity results give rise to the existence of ground state solutions provided that g has a general subcritical growth at infinity. We also conceive a newbiharmonic logarithmic Sobolev inequality

\int_{R^{N}} | u |^{2} \log | u | d x \leq \frac{N}{8} \log (C \int_{R^{N}} | Δ u |^{2} d x), for u \in H^{2} (R^{N}), \int_{R^{N}} u^{2} d x = 1,

for a constant

0 < C < {(\frac{2}{π e N})}^{2}

and we characterize its minimizers.

Zugehörige Institution(en) am KIT	Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp	Forschungsbericht/Preprint
Publikationsmonat/-jahr	07.2021
Sprache	Englisch
Identifikator	ISSN: 2365-662X KITopen-ID: 1000135513
Verlag	Karlsruher Institut für Technologie (KIT)
Umfang	21 S.
Serie	CRC 1173 Preprint ; 2021/32
Projektinformation	SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen	Siehe auch
Schlagwörter	nonlinear scalar field equation, Brezis-Kato reqularity, biharmonic logarithmic Sobolev inequality, critical point theory, Pohozaev manifold
Nachgewiesen in	OpenAlex

KITopen-Download

Volltext

DOI: 10.5445/IR/1000135513

Veröffentlicht am 19.07.2021

Export

Statistiken

Seitenaufrufe: 96
seit 20.07.2021

Downloads: 79
seit 22.07.2021

Repository KITopen

Biharmonic nonlinear scalar field equations

Abstract: