Gehring

Gehring is a surname of German origin. It is found among individuals in German-speaking regions and in communities around the world through migration and diaspora. As a family name, Gehring has appeared across a wide range of professions, including science, the arts, sports, and academia, reflecting broader patterns of Germanic naming traditions.

In mathematics, Gehring's lemma is a notable use of the name. Named after a German mathematician with the surname Gehring, the lemma is a fundamental result in harmonic analysis and regularity theory. It states that if a nonnegative function satisfies a reverse Hölder inequality on a domain, then there exists a higher exponent for which the function also satisfies a reverse Hölder inequality locally. This enhanced integrability property is instrumental in studying the behavior of solutions to elliptic partial differential equations and in the theory of quasiconformal mappings. Gehring's lemma is widely cited as a key tool in analysis and has influenced various approaches to proving regularity results in mathematical contexts.

Beyond its mathematical usage, Gehring serves as a standard German surname encountered in genealogical and historical records. The name thus functions both as a personal identifier and, in academic literature, as the eponym of an important mathematical concept.