×

zbMATH — the first resource for mathematics

The Dirichlet problem with mean curvature operator in Minkowski space – a variational approach. (English) Zbl 1305.35030
Adv. Nonlinear Stud. 14, No. 2, 315-326 (2014); corrigendum ibid. 16, No. 1, 173-174 (2016).
This paper deals with a class of nonlinear variational problems with Dirichlet boundary condition and bounded nonlinearity. The main feature of the present paper is the study in the Minkowski space. By means of variational arguments, the authors establish several qualitative results. An application to the study of nontrivial solutions for a class of nonlinear Dirichlet problems depending on a parameter is provided in the final part of this paper.

MSC:
35J20 Variational methods for second-order elliptic equations
49J40 Variational inequalities
49J52 Nonsmooth analysis
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bartnik, Spacelike hypersurfaces with prescribed boundary values and mean curvature, Math Phys pp 87– (1982) · Zbl 0512.53055
[2] Bereanu, erban Nontrivial solutions for a class of one - parameter problem with singular {\(\phi\)} - Laplacian, Univ Buchar Math Ser pp 61– (2012)
[3] Heinonen, Lectures on Lipschitz Analysis Jyva skyla Dept, Rep Univ Math Stat pp 100– (2005)
[4] Ambrosetti, Dual variational methods in critical point theory and applications, Funct Anal 14 pp 349– (1973) · Zbl 0273.49063
[5] Bereanu, Positive radial solutions for Dirichlet problems with mean cur - vature operators in Minkowski space, Funct Anal pp 264– (2013)
[6] Corsato, Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space, Math Anal Appl pp 405– (2013) · Zbl 1310.35140
[7] Coffman, A prescribed mean curvature problem on domains without radial sym - metry SIAM Maximal spacelike hypersurfaces in the Lorentz - Minkowski spaces of, Math Anal Math 22 pp 982– (1991)
[8] Lieb, Analysis Graduate Studies in Mathematics Provi - dence Rhode Island, Amer Math Soc 14 (2001)
[9] Lo, pez Stationary surfaces in Lorentz - Minkowski space, Proc Royal Soc Edinburgh pp 138– (2008)
[10] Bereanu, Variational methods for nonlinear perturbations of singular {\(\phi\)} - Laplacians, Rend Lincei Mat Appl 22 pp 89– (2011) · Zbl 1219.35062
[11] Alı, as On the Gaussian curvature of maximal surfaces and the Calabi - Bernstein theorem, Bull London Math Soc pp 33– (2001)
[12] Flaherty, The boundary value problem for maximal hypersurfaces, Proc Natl Acad Sci USA pp 4765– (1979) · Zbl 0428.49031
[13] Gidas, Symmetry and related properties via the maximum principle, Math Phys pp 68– (1979) · Zbl 0425.35020
[14] Bereanu, Multiple positive radial solutions for a Dirichlet problem involv - ing the mean curvature operator in Minkowski space, Funct Anal pp 265– (2013)
[15] Coelho, Positive radial solutions of the Dirichlet problem for the Minkowski - curvature equation in a ball Topological Meth Nonlinear to appear, Anal
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.