Variational methods form a fundamental toolkit for analysing nonlinear elliptic equations by recasting boundary value problems as questions about critical points of suitably defined energy functionals ...

Sharp regularity results for minimisers of double phase functionals with variable exponents have been extended beyond the constant exponent case. Under mild continuity assumptions on the exponent ...

Calculus to the level of ODEs, partial derivative and multiple integrals, some knowledge of PDEs helpful but not essential. Students should have a certain comfort level with dealing with advanced ...