We prove existence of solutions for a class of singular elliptic problems with a general measure as source term whose model is
DOI: 10.1051/cocv/2015004
Keywords: Nonlinear elliptic equations, singular elliptic equations, measure data
@article{COCV_2016__22_1_289_0, author = {Oliva, Francescantonio and Petitta, Francesco}, title = {On singular elliptic equations with measure sources}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {289--308}, publisher = {EDP-Sciences}, volume = {22}, number = {1}, year = {2016}, doi = {10.1051/cocv/2015004}, zbl = {1337.35060}, mrnumber = {3489386}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2015004/} }
TY - JOUR AU - Oliva, Francescantonio AU - Petitta, Francesco TI - On singular elliptic equations with measure sources JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 289 EP - 308 VL - 22 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015004/ DO - 10.1051/cocv/2015004 LA - en ID - COCV_2016__22_1_289_0 ER -
%0 Journal Article %A Oliva, Francescantonio %A Petitta, Francesco %T On singular elliptic equations with measure sources %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 289-308 %V 22 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015004/ %R 10.1051/cocv/2015004 %G en %F COCV_2016__22_1_289_0
Oliva, Francescantonio; Petitta, Francesco. On singular elliptic equations with measure sources. ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 1, pp. 289-308. doi : 10.1051/cocv/2015004. http://archive.numdam.org/articles/10.1051/cocv/2015004/
Existence and nonexistence of solutions for singular quadratic quasilinear equations. J. Differ. Equ. 246 (2009) 4006–4042. | DOI | MR | Zbl
, , , , and ,Multiplicity of solutions for a Dirichlet problem with a strongly singular nonlinearity. Nonlinear Analysis 95 (2014) 281–291. | DOI | MR | Zbl
and ,Bifurcation for quasilinear elliptic singular BVP. Commun. Partial Differ. Equ. 36 (2011) 670–692. | DOI | MR | Zbl
, and ,An theory of existence and uniqueness of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa 22 (1995) 240–273. | Numdam | MR | Zbl
, , , , and ,Dirichlet problems with singular and gradient quadratic lower order terms. ESAIM: COCV 14 (2008) 411–426. | Numdam | MR | Zbl
,Some properties of solutions of some semilinear elliptic singular problems and applications to the G-convergence. Asymptotic Analysis 86 (2014) 1–15. | DOI | MR | Zbl
and ,Non-linear elliptic and parabolic equations involving measure data. J. Funct. Anal. 87 (1989) 149–169. | DOI | MR | Zbl
and ,Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Nonlinear Analysis 19 (1992) 581–597. | DOI | MR | Zbl
and ,Semilinear elliptic equations with singular nonlinearities. Calc. Var. Partial Differ. Equ. 37 (2010) 363–380. | DOI | MR | Zbl
and ,Existence of bounded solutions for nonlinear unilateral problems. Ann. Mat. Pura Appl. 152 (1988) 183–196. | DOI | MR | Zbl
, and ,Some simple nonlinear PDE’s without solutions. Bollettino dell’Unione Matematica Italiana Serie 8 (1998) 223–262. | MR | Zbl
and ,H. Brezis, M. Marcus and A.C. Ponce, Nonlinear elliptic equations with measures revisited. Vol. 163 of Ann. Math. Stud. Princeton University Press NJ (2007) 55–110. | MR | Zbl
Minimax methods for singular elliptic equations with an application to a jumping problem. J. Differ. Equ. 221 (2006) 210–223. | DOI | MR | Zbl
,A variational approach to a class of singular semilinear elliptic equations. J. Convex Analysis 11 (2004) 147–162. | MR | Zbl
and ,Symmetry of solutions of some semilinear elliptic equations with singular nonlinearities. J. Differ. Equ. 255 (2013) 4437–4447. | DOI | MR | Zbl
, and ,On a Dirichlet problem in bounded domains with singular nonlinearity. Discrete Contin. Dyn. Syst. 33 (2013) 4923–4944. | DOI | MR | Zbl
and ,On a dirichlet problem with a singular nonlinearity. Commun. Partial. Differ. Equ. 2 (1977) 193–222. | DOI | MR | Zbl
, and ,Renormalized solutions of elliptic equations with general measure data. Annali della Scuola Normale Superiore di Pisa 28 (1999) 741–808. | Numdam | MR | Zbl
, , and ,Nonlinear elliptic equations with singular nonlinearities. Asymptotic Anal. 84 (2013) 181–195. | DOI | MR | Zbl
,D. Giachetti, P. J. Martínez-Aparicio and F. Murat, Elliptic equations with mild singularities: existence and homogenization. Preprint (2015). | arXiv | MR
D. Giachetti, P. J. Martínez-Aparicio and F. Murat, Homogenization of singular semilinear elliptic equations in domains with small holes (preprint).
S. Segura de Leon, A priori estimates for elliptic problems with a strongly singular gradient term and a general datum. Differ. Int. Equ. 26 (2013) 913–948. | MR | Zbl
, ,On a singular nonlinear elliptic boundary-value problem. Proc. Amer. Math. Soc. 111 (1991) 721–730. | DOI | MR | Zbl
and ,Quelques résultats de Višik sur les problémes elliptiques semilinéaires par les méthodes de Minty et Browder. Bull. Soc. Math. France 93 (1965) 97–107. | DOI | Numdam | MR | Zbl
and ,The sub-supersolution method for weak solutions. Proc. Amer. Math. Soc. 136 (2008) 2429–2438. | DOI | MR | Zbl
and ,A. C. Ponce, Selected problems on elliptic equations involving measures. Preprint (2014). | arXiv
Pathological solutions of elliptic differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1964) 385–387. | Numdam | MR | Zbl
,Le problème de Dirichlet pour les équations elliptiques du seconde ordre à coefficientes discontinus. Ann. Inst. Fourier (Grenoble) 15 (1965) 189–258. | DOI | Numdam | MR | Zbl
,The role of the power 3 for elliptic equations with negative exponents. Calc. Var. Partial Differ. Equ. 49 (2014) 909–922. | DOI | MR | Zbl
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