Monotonicity Methods in Hilbert Spaces and Some Applications to Nonlinear Partial Differential Equations

Publisher Summary This chapter discusses the monotonicity methods in Hilbert spaces and presents some applications to nonlinear partial differential equations. It describes classical properties of maximal monotone operators in Hilbert spaces. It focuses on a particular class of monotone operators, namely those that are gradients of convex functions. The chapter also highlights their specific properties that do not hold for general monotone operators. Evolution equations associated with gradients of convex functions: smoothing effect on the initial data, behavior at infinity, and so on are discussed in the chapter along with some applications to nonlinear partial differential equations.

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