1,721,135 research outputs found
Minimization problems with singular data
No full textThis work contains a survey of some results on minimization problems with singular data and some new contributions (not previously published) presented in my lecture at the "Seminario Matematico e Fisico di Milano". © Birkhäuser Verlag, Basel 2006
T-minima
No full textThanks to a suitable definition of minima involving the truncations (T-minima), we study the minimization of functionals, whose model is (Omega)integral b(x,v)vertical bar del v vertical bar(2) - (Omega)integral f(x)v(x), f is an element of L-1
Integral inequalities and summability of solutions of some differential problems.
No full textThe aim of this note is to indicate how inequalities concerning the integral of on the subsets where |u(x)| is greater than k () can be used in order to prove summability properties of u (joint work with Daniela Giachetti). This method was introduced by Ennio De Giorgi and Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems. In some joint works with Thierry Gallouet, inequalities concerning the integral of on the subsets where |u(x)| is less than k () or where k ≤ |u(x)| < k+1 were used in order to prove estimates in Sobolev spaces larger than for solutions of Dirichlet problems with irregular data
Quasilinear elliptic equations with natural growth terms: the regularizing effect of the lower order terms
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Lewy-Stampacchia inequality in quasilinear unilateral problems and application to the G-convergence
No full textThe Fatou lemma approach to the existence in quasilinear elliptic equations with natural growth terms
No full textIn this article, we give a new proof of the existence of bounded solutions for the problem {-div(M(x, u)Du) + mu u = B(x, u, Du) + f(x) in Omega, u=0 on partial derivative Omega using the method introduced in Boccardo et al. [Existence de solutions non bornees pour certaines equations quasi lineaires, Portugaliae Math. 41 (1982), pp. 507-534] and developed in Boccardo [Dirichlet problems with singular and gradient quadratic lower order terms, ESAIM: Control. Optim. Calc. Var. 14 (2008), pp. 411-426], even if here we do not assume a sign condition on the quadratic lower order term B(x, u, Du). A case yielding unbounded solutions will be studied as well
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