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Ghosh, Sekhar
- Elliptic Partial Differential Equation Involving a Singularity and a Radon Measure
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Authors
Affiliations
1 Department of Mathematics, National Institute of Technology, Rourkela, IN
1 Department of Mathematics, National Institute of Technology, Rourkela, IN
Source
The Journal of the Indian Mathematical Society, Vol 86, No 1-2 (2019), Pagination: 95-117Abstract
The aim of this paper is to prove the existence of solution for a partial differential equation involving a singularity with a general nonnegative, Radon measure μ as its nonhomogenous term which is given as−Δu = f(x)h(u) + μ in Ω,
u = 0 on ∂Ω,
u > 0 on Ω,
where Ω is a bounded domain of RN, f is a nonnegative function over Ω.Keywords
Elliptic PDE, Sobolev Space, Schauder Fixed Point Theorem
References
- D. Arcoya, J. Carmona, T. Leonori, P. J. Martinez-Aparicio, L. Orsina and F. Petitta, Existence and nonexistence of solutions for singular quadratic quasilinear equations, Journal of Differential Equations, 246 (2009), 4006-4042.
- P. Benilan, L. Boccardo, T. Gallouet, R. Gariepy, M. Pierre and J. L. Vazquez, An L1 theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa, 22 (1995), 241-273.
- M. Bhakta and M. Marcus, Reduced limit for semilinear boundary value problems with measure data, J. Differential Equations, 256 (2014), 2691-2710.
- L. Boccardo and L. Orsina, Semilinear elliptic equations with singular nonlinearities, Calc. Var., 37 (2010), 363-380.
- H. Brezis and X. Cabre, Some simple nonlinear PDE’s without solutions, Bollettino dell’Unione Matematica Italiana, Serie 8, 1-B (1998), 223-262.
- A. Canino, Minimax methods for singular elliptic equations with an application to a jumping problem, Journal of Differential Equations, 221(1) (2006), 210-223.
- A. Canino and M. Degiovanni, A variational approach to a class of singular semilinear elliptic equations, Journal of Convex Analysis, 11 (2004), 147-162.
- A. Canino, M. Grandinetti and B. Sciunzi, Symmetry of solutions of some semilinear elliptic equations with singular nonlinearities, Journal of Differential Equations, 255 (2013), 4437-4447.
- L. M. De Cave and F. Oliva, Elliptic equations with general singular lower order term and measure data, Nonlinear Analysis, 128 (2015), 391-411.
- L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Providence (2010).
- G. B. Folland, Real analysis (Modern techniques and their applications), Second edition, A Wiley-Interscience publication, 2nd Edition.
- J. A. Gatica, V. Oliker and P. Waltman, Singular nonlinear boundary-value problems for second-order ordinary differential equations, Journal of Differential Equations, 79(1) (1989), 62-78.
- D. Giachetti, P. J. Martinez-Aparicio and F. Murat, A semilinear elliptic equation with a mild singularity at u = 0: Existence and homogenization, Journal de Mathematiques Pures et Appliquees, 107 (2017), 41-77.
- D. Giachetti, P. J. Martinez-Aparicio and F. Murat, Definition, existence, stability and uniqueness of the solution to a semilinear elliptic problem with a strong singularity at u = 0, Annali della Scuola Normale Superiore di Pisa, 2017.
- A. C. Lazer and P. J. McKenna, On a singular nonlinear elliptic boundary-value problem, Proc. Amer. Math. Soc., 111(3) (1991), 721-730.
- J. Leray and J. L. Lions, Quelques resultats de Visik sur les problemes elliptiques non lineaires par les methodes de Minty-Browder, Bulletin de la S.M.F., 93 (1965), 97-107.
- M. Marcus and L. Veron, Nonlinear second order elliptic equations involving measures, de Gruyter Series in Nonlinear Analysis and Applications, 21 (2013).
- M. Montenegro and A. C. Ponce, The sub-supersolution method for weak solutions, Proc. Amer. Math. Soc., 136(7) (2008), 2429-2438.
- F. Oliva and F. Petitta, Finite and infinite energy solutions of singular elliptic problems: Existence and Uniqueness, Journal of Differential Equations, 264 (2018), 311-340.
- F. Oliva and F. Petitta, On singular elliptic equations with measure sources, ESAIM: Control, Optimisation and Calculus of Variations, 22 (2016), 289-308.
- G. Stampacchia, Le probleme de Dirichlet pour lesequations elliptiques du second ordre a coefficientes discontinus, Annales de l'institut Fourier, 15(1) (1965), 189-257.
- Y. Sun and D. Zhang, The role of the power 3 for elliptic equations with negative exponents, Calculus of Variations, 49 (2014), 909-922.
- S. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Analysis, Theory, Methods & Applications, 3(6) (1979), 897-904.