The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450. It is awarded every three years for a notable research work in analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000.
In the mathematical fields of partial differential equations and geometric analysis, the maximum principle is any of a collection of results and techniques of fundamental importance in the study of elliptic and parabolic differential equations.
Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
Luis Ángel Caffarelli is an Argentine–American mathematician. He studies partial differential equations and their applications.
Lawrence Craig Evans is an American mathematician and Professor of Mathematics at the University of California, Berkeley.
Shiu-Yuen Cheng (鄭紹遠) is a Hong Kong mathematician. He is currently the Chair Professor of Mathematics at the Hong Kong University of Science and Technology. Cheng received his Ph.D. in 1974, under the supervision of Shiing-Shen Chern, from University of California at Berkeley. Cheng then spent some years as a post-doctoral fellow and assistant professor at Princeton University and the State University of New York at Stony Brook. Then he became a full professor at University of California at Los Angeles. Cheng chaired the Mathematics departments of both the Chinese University of Hong Kong and the Hong Kong University of Science and Technology in the 1990s. In 2004, he became the Dean of Science at HKUST. In 2012, he became a fellow of the American Mathematical Society.
In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of u and in the second-order partial derivatives of u. The independent variables (x,y) vary over a given domain D of R2. The term also applies to analogous equations with n independent variables. The most complete results so far have been obtained when the equation is elliptic.
Leon Melvyn Simon, born in 1945, is a Leroy P. Steele Prize and Bôcher Prize-winning mathematician, known for deep contributions to the fields of geometric analysis, geometric measure theory, and partial differential equations. He is currently Professor Emeritus in the Mathematics Department at Stanford University.
Sergiu Klainerman is a mathematician known for his contributions to the study of hyperbolic differential equations and general relativity. He is currently the Eugene Higgins Professor of Mathematics at Princeton University, where he has been teaching since 1987.
In differential geometry, the Minkowski problem, named after Hermann Minkowski, asks for the construction of a strictly convex compact surface S whose Gaussian curvature is specified. More precisely, the input to the problem is a strictly positive real function ƒ defined on a sphere, and the surface that is to be constructed should have Gaussian curvature ƒ(n(x)) at the point x, where n(x) denotes the normal to S at x. Eugenio Calabi stated: "From the geometric view point it [the Minkowski problem] is the Rosetta Stone, from which several related problems can be solved."
In mathematics, the Hopf lemma, named after Eberhard Hopf, states that if a continuous real-valued function in a domain in Euclidean space with sufficiently smooth boundary is harmonic in the interior and the value of the function at a point on the boundary is greater than the values at nearby points inside the domain, then the derivative of the function in the direction of the outward pointing normal is strictly positive. The lemma is an important tool in the proof of the maximum principle and in the theory of partial differential equations. The Hopf lemma has been generalized to describe the behavior of the solution to an elliptic problem as it approaches a point on the boundary where its maximum is attained.
In mathematics, k-Hessian equations are partial differential equations (PDEs) based on the Hessian matrix. More specifically, a Hessian equation is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix. When k ≥ 2, the k-Hessian equation is a fully nonlinear partial differential equation. It can be written as , where , , and , are the eigenvalues of the Hessian matrix and , is a th elementary symmetric polynomial.
Henri Berestycki is a French mathematician who obtained his PhD from Université Paris VI – Université Pierre et Marie Curie in 1975. His Dissertation was titled Contributions à l'étude des problèmes elliptiques non linéaires, and his doctoral advisor was Haim Brezis. He was an L.E. Dickson Instructor in Mathematics at the University of Chicago from 1975–77, after which he returned to France to continue his research. He has made many contributions in nonlinear analysis, ranging from nonlinear elliptic equations, hamiltonian systems, spectral theory of elliptic operators, and with applications to the description of mathematical modelling of fluid mechanics and combustion. His current research interests include the mathematical modelling of financial markets, mathematical models in biology and especially in ecology, and modelling in social sciences. For these latter topics, he obtained an ERC Advanced grant in 2012.
Robert V. Kohn is an American mathematician working on partial differential equations, calculus of variations, mathematical materials science, and mathematical finance. He is a professor at the Courant Institute of Mathematical Sciences, New York University.
Validated numerics, or rigorous computation, verified computation, reliable computation, numerical verification is numerics including mathematically strict error evaluation, and it is one field of numerical analysis. For computation, interval arithmetic is used, and all results are represented by intervals. Validated numerics were used by Warwick Tucker in order to solve the 14th of Smale's problems, and today it is recognized as a powerful tool for the study of dynamical systems.
Walter Alexander Strauss is American applied mathematician, specializing in partial differential equations and nonlinear waves. His Research interests are Partial Differential Equations, Mathematical Physics, Stability Theory, Solitary Waves, Kinetic Theory of Plasmas, Scattering Theory, Water Waves, Dispersive Waves.
Xavier Ros Oton is a Spanish mathematician who works on partial differential equations (PDEs). He is an ICREA Research Professor and a Full Professor at the University of Barcelona.
Joel Spruck is a mathematician, J. J. Sylvester Professor of Mathematics at Johns Hopkins University, whose research concerns geometric analysis and elliptic partial differential equations. He obtained his PhD from Stanford University with the supervision of Robert S. Finn in 1971.
Wei-Ming Ni is a Taiwanese mathematician at the University of Minnesota and the Chinese University of Hong Kong, and the former director of the Center for PDE at the East China Normal University. He works in the field of elliptic and parabolic partial differential equations. He did undergraduate work at National Taiwan University and obtained his Ph.D. at New York University, in 1979, under the supervision of Louis Nirenberg. He is an editor-in-chief of the Journal of Differential Equations, and was an ISI Highly Cited Researcher in 2002. As said by the journal Discrete and Continuous Dynamical Systems:
[Ni] first became a household name in the PDE community when he published with Gidas and Nirenberg the seminal paper in 1979, “On the symmetry of positive solutions of nonlinear elliptic equations” [...] The research and expository work of Professor Ni has influenced the research directions and activities of a large number of mathematicians, many of whom are playing important roles in the field of partial differential equations today.
YanYan Li is a Professor of mathematics at Rutgers University, specializing in elliptic partial differential equations. He received his Ph.D. at New York University in 1988, under the direction of Louis Nirenberg. He joined Rutgers University in 1990.
