Detailed Proof of Classical Gagliardo–Nirenberg Interpolation Inequality with Historical Remarks
Alberto FiorenzaUniversità di Napoli Federico II, Italy
Maria Rosaria FormicaUniversità di Napoli Parthenope, Italy
Tomáš G. RoskovecUniversity of South Bohemia, České Budějovice and Czech Technical University, Prague, Czechia
Filip SoudskýUniversity of South Bohemia, České Budějovice, Czechia
A carefully written Nirenberg's proof of the famous Gagliardo–Nirenberg interpolation inequality for intermediate derivatives in seems, surprisingly, to be missing in literature. In our paper, we shall first introduce this fundamental result and provide information about its historical background. Afterwards, we present a complete, student-friendly proof. In our proof, we use the architecture of Nirenberg's argument, the explanation is, however, much more detailed, also containing some differences. The reader can find a short comparison of differences and similarities in the final chapter.
Cite this article
Alberto Fiorenza, Maria Rosaria Formica, Tomáš G. Roskovec, Filip Soudský, Detailed Proof of Classical Gagliardo–Nirenberg Interpolation Inequality with Historical Remarks. Z. Anal. Anwend. 40 (2021), no. 2, pp. 217–236DOI 10.4171/ZAA/1681