Recent decades have witnessed a bloom in research at the interface of complex geometry and nonlinear partial differential equations. This interdisciplinary field explores the deep and intricate ...

We show that any entire solution of an essentially nonlinear first-order partial differential equation in two variables must be linear. Journal Information This monthly journal, begun in 1950, is ...

We consider a specific type of nonlinear partial differential equation (PDE) that appears in mathematical finance as the result of solving some optimization problems. We review some examples of such ...

This book serves as a bridge between graduate textbooks and research articles in the area of nonlinear elliptic partial differential equations. Whereas graduate textbooks present basic concepts, the ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

We derive a partial differential equation (PDE) representation for the value of financial derivatives with bilateral counterparty risk and funding costs. The model is very general in that the funding ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...