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...Calculus of variations and partial dierential equations diogo aguiar gomes contents introduction finite dimensional optimization problems n unconstrained minimization in r convexity lagrange multipliers linear programming non with constraints bibliographical notes one independent variable euler further necessary conditions applications to riemannian geometry hamiltonian dynamics sucient symmetries noether theorem critical point theory invariant measures convex systems perturbation elliptic equation direct method the regularity by energy methods h older continuity schauder estimates optimal control viscosity solutions elementary examples properties dynamic principle pontryagin maximum hamilton jacobi verication existence controls bounded space sub superdierentials setting stationary duality model some informal computations generalized mather problem monge kantorowich bibliography index...