{"product_id":"the-effect-of-a-singular-markus-lilli-9783832509286","title":"The Effect of a Singular Perturbation to a 1-D Non-Convex Variational Problem","description":"Nonconvex variational problems are of importance in modeling problems of microstructures and elasticity. In this book, we consider a $1$-d nonconvex problem and we prove existence of solutions of the corresponding non-elliptic Euler-Lagrange equation by considering the Euler-Lagrange equation of the singular perturbed variational problem and passing to the limit. Under general assumptions on the potential we prove existence of Young-measure solutions. More restrictive conditions on the potential yield classical solutions via a topological method. The singular perturbed problem, which is also of interest for physicists due to the higher gradient surface-energy, is discussed in big detail.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Markus LILLI\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3832509283\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783832509286\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Logos Verlag Berlin\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 11\/15\/2005\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 100\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback","brand":"Markus LILLI","offers":[{"title":"Paperback","offer_id":48450114191615,"sku":"9783832509286","price":61.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_5386c2ee-2c2b-4622-968d-79ed4d1406f0.jpg?v=1777266274","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-effect-of-a-singular-markus-lilli-9783832509286","provider":"WR Book House","version":"1.0","type":"link"}