{"product_id":"the-effect-of-a-singular-perturbation-to-a-1-d-non-convex-variational-problem-paperback","title":"The Effect of a Singular Perturbation to a 1-D Non-Convex Variational Problem - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eMarkus LILLI\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eNonconvex 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.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 100\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.33 x 7.96 x 5.68 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e February 19, 2014\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":46661638521029,"sku":"9783832509286","price":121.19,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0757\/6718\/5605\/files\/jn-DmtfXL09783832509286.webp?v=1785907711","url":"https:\/\/selloorium.com\/products\/the-effect-of-a-singular-perturbation-to-a-1-d-non-convex-variational-problem-paperback","provider":"Selloorium","version":"1.0","type":"link"}