We study the summability up to the boundary of the second derivatives of solutions to a class of Dirichlet boundary value problems involving the p-Laplace operator. Our results are meaningful for the cases when the Hopf’s Lemma cannot be applied to ensure that there are no critical points of the solution on the boundary of the domain.
Mots clés : p-Laplace equations, regularity of the solutions
@article{COCV_2018__24_2_849_0,
author = {Riey, Giuseppe and Sciunzi, Berardino},
title = {A note on the boundary regularity of solutions to quasilinear elliptic equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {849--858},
publisher = {EDP-Sciences},
volume = {24},
number = {2},
year = {2018},
doi = {10.1051/cocv/2017040},
zbl = {1403.35118},
mrnumber = {3816418},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2017040/}
}
TY - JOUR AU - Riey, Giuseppe AU - Sciunzi, Berardino TI - A note on the boundary regularity of solutions to quasilinear elliptic equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 849 EP - 858 VL - 24 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017040/ DO - 10.1051/cocv/2017040 LA - en ID - COCV_2018__24_2_849_0 ER -
%0 Journal Article %A Riey, Giuseppe %A Sciunzi, Berardino %T A note on the boundary regularity of solutions to quasilinear elliptic equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 849-858 %V 24 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017040/ %R 10.1051/cocv/2017040 %G en %F COCV_2018__24_2_849_0
Riey, Giuseppe; Sciunzi, Berardino. A note on the boundary regularity of solutions to quasilinear elliptic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 849-858. doi : 10.1051/cocv/2017040. http://archive.numdam.org/articles/10.1051/cocv/2017040/
[1] and , Regularity, monotonicity and symmetry of positive solutions of m-Laplace equations. J. Differ. Equ. 206 (2004) 483–515 | DOI | MR | Zbl
[2] and , Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of m-Laplace equations. Calc. Var. Partial Differ. Equ. 25 (2006) 139–159 | DOI | MR | Zbl
[3] C1+α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 7 (1983) 827–850 | DOI | MR | Zbl
[4] , and , Monotonicity of solutions of quasilinear degenerate elliptic equations in half-spaces. Math. Ann. 357 (2013) 855–893 | DOI | MR | Zbl
[5] , , and , Concentration of solutions for some singularly perturbed mixed problems: asymptotics of minimal energy solutions. Ann. Inst. H. Poincar Anal. Non Lineare 27 (2010) 37–56 | DOI | Numdam | MR | Zbl
[6] and , Universal potential estimates. J. Funct. Anal. 262 (2012) 4205–4269 | DOI | MR | Zbl
[7] , Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Anal. 12 (1988) 1203–1219 | MR | Zbl
[8] , and , Comparison principles for p-Laplace equations with lower order terms. Ann. Mat. Pura Appl. 196 (2017) 877–903 | DOI | MR | Zbl
[9] , , and , Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the Hardy-Leray potential. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014) 1–22 | DOI | Numdam | MR | Zbl
[10] , and , A regularity result for the p-Laplacian near uniform ellipticity. SIAM J. Mathe. Anal. 48 (2016) 2059–2075 | DOI | MR | Zbl
[11] and , H = W. Proc. Nat. Acad. Sci. USA 51 (1964) 1055–1056 | DOI | MR | Zbl
[12] S. Merchan, L. Montoro and B. Sciunzi, On the Harnack inequality for quasilinear elliptic equations with a first order term. Proceedings of the Royal Society of Hedinburg. Section A. Mathematics, to appear | MR
[13] , and , Asymptotic symmetry for a class of quasi-linear parabolic problems. Adv. Nonl. Studies 10 (2010) 789–818 | DOI | MR | Zbl
[14] , Regularity of minima: an invitation to the dark side of the calculus of variations. Appl. Math. 51 (2006) 355–426 | DOI | MR | Zbl
[15] , The Calderon-Zygmund theory for elliptic problemswith measure data. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 6 (2007) 195–261 | Numdam | MR | Zbl
[16] and , Boundary value problems for some degenerate-elliptic operators. Ann. Mat. Pura Appl. 80 (1968) 1–122 | DOI | MR | Zbl
[17] , Some results on the qualitative properties of positive solutions of quasilinear elliptic equations. NoDEA. Nonlinear Differ. Equ. Appl. 14 (2007) 315–334 | DOI | MR | Zbl
[18] , Regularity and comparison principles for p-Laplace equations with vanishing source term. Commun. Cont. Math. 16 (2014) 1450013, 20 | DOI | MR | Zbl
[19] , Regularity for a more general class of quasilinear elliptic equations. J. Differ. Equ. 51 (1984) 126–150 | DOI | MR | Zbl
[20] , Regularity for quasilinear equations on degenerate singular sets. Math. Ann. 358 (2014) 241–256 | DOI | MR | Zbl
[21] , Linear elliptic operators with measurable coefficients. Ann. Scuola Norm. Sup. Pisa 27 (1973) 265–308 | Numdam | MR | Zbl
Cité par Sources :
