{"product_id":"9783832509286","title":"The Effect of a Singular Perturbation to a 1-d Non-Convex Variational Problem","description":"\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","brand":"Logos Verlag","offers":[{"title":"Default Title","offer_id":47062689710320,"sku":"9783832509286","price":61.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9783832509286_p0.jpg?v=1763687085","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9783832509286","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}