Unveiling the Power of Nonlinear Dirichlet Forms

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The exploration of multivalued operators and subgradients of convex functionals initiated in the 1960s laid the groundwork for understanding nonlinear problems through bilinear forms. This approach revealed significant connections between subgradients and semigroups, particularly in the context of nonlinear accretive operators. The development of this theory, particularly on Hilbert and later Banach spaces, demonstrated surprising similarities to linear theories. Notably, it established that certain convex maps generate semigroups of Lipschitz continuous contractions, providing solutions to abstract Cauchy problems.