Erik Albert Holmgren

Erik Albert Holmgren (* July 7, 1872, † March 18, 1943 ) was a Swedish mathematician who was concerned with partial differential equations.

Holmgren was the son of the mathematician Hjalmar Holmgren (1822-1885), a professor at the Technical University of Stockholm. Holmgren in 1898 received his doctorate at the University of Uppsala on differential equations. He was from 1909 to 1937 professor in Uppsala. In 1924 he became a member of the Academy of Sciences in Uppsala.

He is known for Holmgren 's uniqueness theorem for linear partial differential equations with real analytic coefficients. He says that a solution of the Cauchy problem ( with Cauchy data on a non - characteristic surface S) in the vicinity of S has a unique solution. The sentence tightened so that leaves open the ( general valid) set of Cauchy- Kovalevskaya in the linear case, which ensures the existence of an analytical solution and the existence of non-analytic solutions. By the theorem of Holmgren there are no other solutions in the linear case.

His doctoral counts Torsten Carleman.