{"product_id":"unveiling-the-power-of-nonlinear-dirichlet-forms-von-class","title":"Unveiling the Power of Nonlinear Dirichlet Forms","description":"Beginning in the 60s, Rockafellar and others [BR65, Mor63, Roc70a, Roc70b, RW98] introduced and studied multivalued operators and subgradients of convex functionals. In fact, it is easy to show that the subgradient ∂Eb of Eb is equal to B. Hence, there is a direct connection between Eb,B and the semigroup S generated by B, without mentioning the original bilinear form.\nStudying bilinear forms by studying the energy has a major advantage. While bilinear forms are always associated with linear operators, subgradients of arbitrary, not necessarily quadratic, energies are not. This approach led to a new way of investigating a large class of nonlinear problems. In the 60s and 70s Brezis, Crandall, Pazy and others developed a theory of nonlinear accretive operators and nonlinear semigroups, first on Hilbert spaces [Lio69, BP72, Kat67, Bre73] and later on also on Banach spaces [CL71, CP72]. Surprisingly this theory closely resembles the linear theory sketched previously. Among other results, they showed that a proper, convex and lower semicontinuous map E : H → (−∞, ∞] on a Hilbert space H admits a m-accretive subgradient ∂E, which in turn generates a semigroup R of Lipschitz continuous contractions such that t → Rtu0 is the unique mild solution of the abstract Cauchy problem\n∂tu + ∂Eu =0,\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783384254672\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783384254672","offer_id":48871645249861,"sku":"9783384254672","price":28.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/4bdea4f4-84df-4324-938e-47a173eae094.jpg?v=1776485548","url":"https:\/\/shop.autorenwelt.de\/en\/products\/unveiling-the-power-of-nonlinear-dirichlet-forms-von-class","provider":"Autorenwelt Shop","version":"1.0","type":"link"}