Abstract
AbstractIn this work we prove the existence of nontrivial bounded variation solutions to quasilinear elliptic problems involving a weighted 1-Laplacian operator. A key feature of these problems is that weights are unbounded. One of our main tools is the well-known Caffarelli-Kohn-Nirenberg’s inequality, which is established in the framework of weighted spaces of functions of bounded variation (and that provides us the necessary embeddings between weighted spaces). Additional tools are suitable variants of the Mountain Pass Theorem as well as an extension of the pairing theory by Anzellotti to this new setting.
Funder
FAPESP
CNPq
Ministerio de Ciencia, Innovación y Universidades (ES) and FEDER
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference37 articles.
1. Abdellaoui, B., Colorado, E., Peral, I.: Some remarks on elliptic equations with singular potentials and mixed boundary conditions. Adv. Nonlinear Stud. 4(4), 503–533 (2004)
2. Abdellaoui, B., Peral, I.: On quasilinear elliptic equations related to some Caffarelli–Kohn–Nirenberg inequalities. Commun. Pure Appl. Anal. 2(4), 539–566 (2003)
3. Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349–381 (1973)
4. Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford (2000)
5. Andreu, F., Ballester, C., Caselles, V., Mazón, J.M.: Minimizing total variation flow. C. R. Acad. Sci. Paris Sér. I Math., 331(11), 867–872 (2000)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献