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Nonlinear Partial Differential Equations and Variational Methods
The research in this modern area of applied mathematics at Simon Fraser University includes partial differential equations, nonlinear analysis, and the calculus of variations.
Given a nonlinear problem the first question is often: do we have a solution? Fundamentally, this questions involves several connected parts: Does there exist a solution? Is the solution unique? Is the solutions stable under perturbations? To answer these questions often involves restating the question in a broader (called weak) context, where solutions can be found, and then addressing the regularity question: is the weak solution actually strong.
Research into these problems at the theoretical level includes nonlinear elliptic partial differential equations and variational problems. Applications include material science, control theory, and mathematical finance.