Jean Leray was a French mathematician, who worked on both partial differential equations and algebraic topology.
Solomon Lefschetz was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.
In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations.
The Schauder fixed-point theorem is an extension of the Brouwer fixed-point theorem to topological vector spaces, which may be of infinite dimension. It asserts that if is a nonempty convex closed subset of a Hausdorff topological vector space and is a continuous mapping of into itself such that is contained in a compact subset of , then has a fixed point.
Juliusz Paweł Schauder was a Polish mathematician of Jewish origin, known for his work in functional analysis, partial differential equations and mathematical physics.
Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
Mark Alexandrovich Krasnoselsky was a Soviet, Russian and Ukrainian mathematician renowned for his work on nonlinear functional analysis and its applications.
In mathematics, topological degree theory is a generalization of the winding number of a curve in the complex plane. It can be used to estimate the number of solutions of an equation, and is closely connected to fixed-point theory. When one solution of an equation is easily found, degree theory can often be used to prove existence of a second, nontrivial, solution. There are different types of degree for different types of maps: e.g. for maps between Banach spaces there is the Brouwer degree in Rn, the Leray-Schauder degree for compact mappings in normed spaces, the coincidence degree and various other types. There is also a degree for continuous maps between manifolds.
Georges Henri Reeb was a French mathematician. He worked in differential topology, differential geometry, differential equations, topological dynamical systems theory and non-standard analysis.
Paul H. Rabinowitz is the Edward Burr Van Vleck Professor of Mathematics and a Vilas Research Professor at the University of Wisconsin, Madison. He received a Ph.D. from New York University in 1966 under the direction of Jürgen Moser. From 1966 to 1969 he held a position as assistant professor at Stanford University. He has visited many mathematical institutions all over the world. In 1978 Paul Rabinowitz became a fellow of the John Simon Guggenheim Memorial Foundation.
Sir Martin Hairer is an Austrian-British mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at Imperial College London, having previously held appointments at the University of Warwick and the Courant Institute of New York University. In 2014 he was awarded the Fields Medal, one of the highest honours a mathematician can achieve. In 2020 he won the 2021 Breakthrough Prize in Mathematics.
In the theory of partial differential equations, an a priori estimate is an estimate for the size of a solution or its derivatives of a partial differential equation. A priori is Latin for "from before" and refers to the fact that the estimate for the solution is derived before the solution is known to exist. One reason for their importance is that if one can prove an a priori estimate for solutions of a differential equation, then it is often possible to prove that solutions exist using the continuity method or a fixed point theorem.
Pierre Schapira is a French mathematician. He specializes in algebraic analysis, especially Mikio Sato's microlocal analysis, together with the mathematical concepts of sheaves and derived categories.
J. (Jean) François Trèves is a French mathematician, specializing in partial differential equations.
Frank Merle is a French mathematician, specializing in partial differential equations and mathematical physics.
Edward Norman Dancer FAA is an Australian mathematician, specializing in nonlinear analysis.
Roger David Nussbaum is an American mathematician, specializing in nonlinear functional analysis and differential equations.
Gustavo A. Ponce is a Venezuelan mathematician.
Jean-Yves Chemin is a French mathematician, specializing in nonlinear partial differential equations.
In mathematics, the Leray–Schauder degree is an extension of the degree of a base point preserving continuous map between spheres or equivalently to a boundary sphere preserving continuous maps between balls to boundary sphere preserving maps between balls in a Banach space , assuming that the map is of the form where is the identity map and is some compact map.
