field of partial differential equations, Harnack's principle or Harnack's theorem is a corollary of Harnack's inequality which deals with the convergence...

theory. Harnack's inequality applied to harmonic functions. He also worked on the real algebraic geometry of plane curves, proving Harnack's curve theorem...

Arvid Falk Harnack (1913–1991), German anti-Nazi resistance fighter, film and stage director, brother of Arvid Harnack Harnack's principle This page lists...

or principle is a theorem with wide applicability (e.g. the law of large numbers, law of cosines, Kolmogorov's zero–one law, Harnack's principle, the...

he meant Fish-Harnack's tactful approach to the Nazis' increasing incursion into the university in 1931 and 1932. By the time Fish-Harnack arrived in Giessen...

constant functions. In addition to these basic inequalities, one has Harnack's inequality, which states that positive harmonic functions on bounded domains...

Mathematics Institutions University of Zagreb Thesis Special classes of Excessive Functions Satisfying Harnack's Principle  (1990) Doctoral advisor Murali Rao...

Loeb, Peter; Walsh, Bertram (1965). "The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot". Annales de...

assuming f(x) is zero for some unit vector x and f(y) < 0 if |y| < 1. By Harnack's inequality applied to −f − f ( r x ) ≥ − 1 − r ( 1 + r ) n − 1 f ( 0 )...

a bounded domain Ω. Then for every non-negative harmonic function u, Harnack's inequality sup V u ≤ C inf V u {\displaystyle \sup _{V}u\leq C\inf _{V}u}...