In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function.
Dušan D. Repovš is a Slovenian mathematician from Ljubljana, Slovenia.
Elwin Bruno Christoffel was a German mathematician and physicist. He introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus, which would later provide the mathematical basis for general relativity.
Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
In mathematics, the viscosity solution concept was introduced in the early 1980s by Pierre-Louis Lions and Michael G. Crandall as a generalization of the classical concept of what is meant by a 'solution' to a partial differential equation (PDE). It has been found that the viscosity solution is the natural solution concept to use in many applications of PDE's, including for example first order equations arising in dynamic programming, differential games or front evolution problems, as well as second-order equations such as the ones arising in stochastic optimal control or stochastic differential games.
Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled by David Hilbert in 1900. It asks whether the solutions of regular problems in the calculus of variations are always analytic. Informally, and perhaps less directly, since Hilbert's concept of a "regular variational problem" identifies this precisely as a variational problem whose Euler–Lagrange equation is an elliptic partial differential equation with analytic coefficients, Hilbert's nineteenth problem, despite its seemingly technical statement, simply asks whether, in this class of partial differential equations, any solution inherits the relatively simple and well understood property of being an analytic function from the equation it satisfies. Hilbert's nineteenth problem was solved independently in the late 1950s by Ennio De Giorgi and John Forbes Nash, Jr.
In the calculus of variations, a branch of mathematics, a Nehari manifold is a manifold of functions, whose definition is motivated by the work of Zeev Nehari. It is a differentiable manifold associated to the Dirichlet problem for the semilinear elliptic partial differential equation
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.
Michael Struwe is a German mathematician who specializes in calculus of variations and nonlinear partial differential equations. He won the 2012 Cantor medal from the Deutsche Mathematiker-Vereinigung for "outstanding achievements in the field of geometric analysis, calculus of variations and nonlinear partial differential equations".
Maria J. Esteban is a Spanish mathematician. In her research she studies nonlinear partial differential equations, mainly by the use of variational methods, with applications to physics and quantum chemistry. She has also worked on fluid-structure interaction.
Jane Smiley Cronin Scanlon was an American mathematician and an emeritus professor of mathematics at Rutgers University. Her research concerned partial differential equations and mathematical biology.
Gheorghe Moroșanu is a Romanian mathematician known for his works in Ordinary and Partial Differential Equations, Nonlinear Analysis, Calculus of Variations, Fluid Mechanics, Asymptotic Analysis, Applied Mathematics. He earned his Ph.D. in 1981 from the Alexandru Ioan Cuza University in Iași.
Hans Wilhelm Alt is a German mathematician, specializing in partial differential equations and their applications.
Bernold Fiedler is a German mathematician, specializing in nonlinear dynamics.
Edward Norman Dancer FAA is an Australian mathematician, specializing in nonlinear analysis.
Victor Lenard Shapiro was an American mathematician, specializing in trigonometric series and differential equations. He is known for his two theorems on the uniqueness of multiple Fourier series.
Gabriella Tarantello is an Italian mathematician specializing in partial differential equations, differential geometry, and gauge theory. She is a professor in the department of mathematics at the University of Rome Tor Vergata.
Roger David Nussbaum is an American mathematician, specializing in nonlinear functional analysis and differential equations.
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.
Hans-Wilhelm Knobloch was a German mathematician, specializing in dynamical systems and control theory. Although the field of mathematical systems and control theory was already well-established in several other countries, Hans-Wilhelm Knobloch and Diederich Hinrichsen were the two mathematicians of most importance in establishing this field in Germany.
