Detailed Proof of Classical Gagliardo–Nirenberg Interpolation Inequality with Historical Remarks

  • Alberto Fiorenza

    Università di Napoli Federico II, Italy
  • Maria Rosaria Formica

    Università di Napoli Parthenope, Italy
  • Tomáš G. Roskovec

    University of South Bohemia, České Budějovice and Czech Technical University, Prague, Czechia
  • Filip Soudský

    University of South Bohemia, České Budějovice, Czechia
Detailed Proof of Classical Gagliardo–Nirenberg Interpolation Inequality with Historical Remarks cover
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Abstract

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. 217–236

DOI 10.4171/ZAA/1681