Explore the viscosity solutions approach to variational problems in this 55-minute colloquium talk from the Women and Mathematics series. Delve into Laplace's equation, multiple proof methods, and key mathematical concepts as presented by Daniela De Silva from Columbia University. Gain insights into integration by parts, Harnack inequality, Hölder continuity, and hardneck inequality. Examine super solutions, discrete equations, and explicit computations while understanding the motivation behind and contributions to this field of study. Enhance your understanding of advanced mathematical techniques and their applications in solving complex variational problems.