This work is devoted to the study of nonvariational, singularly perturbed elliptic equations of degenerate type. The governing operator is anisotropic and ellipticity degenerates along the set of critical points. The singular behavior is of order along ϵ-level layers , and a non-homogeneous source acts in the noncoincidence region . We obtain the precise geometric behavior of solutions near ϵ-level surfaces, by means of optimal regularity and sharp geometric nondegeneracy. We further investigate Hausdorff measure properties of ϵ-level surfaces. The analysis of the asymptotic limits as the ϵ parameter goes to zero is also carried out. The results obtained are new even if restricted to the uniformly elliptic, isotropic setting.
Mots clés : Singularly perturbed equations, Degenerate fully nonlinear operators, Geometric regularity theory
@article{AIHPC_2017__34_3_655_0,
author = {Ara\'ujo, Dami\~ao J. and Ricarte, Gleydson C. and Teixeira, Eduardo V.},
title = {Singularly perturbed equations of degenerate type},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {655--678},
publisher = {Elsevier},
volume = {34},
number = {3},
year = {2017},
doi = {10.1016/j.anihpc.2016.03.004},
mrnumber = {3633739},
zbl = {1362.35028},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2016.03.004/}
}
TY - JOUR AU - Araújo, Damião J. AU - Ricarte, Gleydson C. AU - Teixeira, Eduardo V. TI - Singularly perturbed equations of degenerate type JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 655 EP - 678 VL - 34 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2016.03.004/ DO - 10.1016/j.anihpc.2016.03.004 LA - en ID - AIHPC_2017__34_3_655_0 ER -
%0 Journal Article %A Araújo, Damião J. %A Ricarte, Gleydson C. %A Teixeira, Eduardo V. %T Singularly perturbed equations of degenerate type %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 655-678 %V 34 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2016.03.004/ %R 10.1016/j.anihpc.2016.03.004 %G en %F AIHPC_2017__34_3_655_0
Araújo, Damião J.; Ricarte, Gleydson C.; Teixeira, Eduardo V. Singularly perturbed equations of degenerate type. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 655-678. doi : 10.1016/j.anihpc.2016.03.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.03.004/
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