Existence results for elliptic problems with gradient terms via a priori estimates

被引：17
|
作者：
Baldelli L. [1 ]
Filippucci R. [2 ]
机构：
[1] Department of Mathematics, University of Firenze, Viale Morgagni 40-44, Firenze
[2] Department of Mathematics, University of Perugia, Via Vanvitelli 1, Perugia
来源：
Nonlinear Analysis, Theory, Methods and Applications | 2020年 / 198卷
关键词：
A priori estimates; Elliptic problems; Gradient terms;
D O I：
10.1016/j.na.2020.111894
中图分类号：
学科分类号：
摘要：
We prove existence of nonnegative solutions of a Dirichlet problem on a bounded smooth domain of RN for a p-Laplacian elliptic equation with a convection term. Our proof is based on a priori bounds for a suitable weighted norm involving the distance function from the boundary, obtained by adapting the technique developed by Barrios et al. [4] for nonlocal elliptic problems, which is a modification of the classical scaling blow up method due to Gidas and Spruck in the celebrated paper [25]. The conclusion then follows by using topological degree. © 2020 Elsevier Ltd
引用
收藏
相关论文
共 50 条
  • [31] Existence results for a class of nonlinear elliptic problems with p-growth in the gradient
    Grenon, N
    Trombetti, C
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (03) : 931 - 942
  • [32] A priori bounds and existence of solutions for some nonlocal elliptic problems
    Barrios, Begona
    Del Pezzo, Leandro
    Garcia-Melian, Jorge
    Quaas, Alexander
    REVISTA MATEMATICA IBEROAMERICANA, 2018, 34 (01) : 195 - 220
  • [33] A Priori Bounds and Existence of Solutions for Slightly Superlinear Elliptic Problems
    Garcia-Melian, J.
    Iturriaga, L.
    Ramos Quoirin, H.
    ADVANCED NONLINEAR STUDIES, 2015, 15 (04) : 923 - 938
  • [34] UNIFORM A PRIORI ESTIMATES FOR ELLIPTIC PROBLEMS WITH IMPEDANCE BOUNDARY CONDITIONS
    Chaumont-Frelet, Theophile
    Nicaise, Serge
    Tomezyk, Jerome
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (05) : 2445 - 2471
  • [35] A priori estimates for elliptic equations with reaction terms involving the function and its gradient (vol 378, pg 13, 2020)
    Bidaut-Veron, Marie-Francoise
    Garcia-Huidobro, Marta
    Veron, Laurent
    MATHEMATISCHE ANNALEN, 2025, 392 (01) : 1481 - 1482
  • [36] Uniform a priori estimates for elliptic and static Maxwell interface problems
    Huang, Jianguo
    Zou, Jun
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2007, 7 (01): : 145 - 170
  • [37] A PRIORI ESTIMATES AND REDUCTION PRINCIPLES FOR QUASILINEAR ELLIPTIC PROBLEMS AND APPLICATIONS
    D'Ambrosio, Lorenzo
    Mitidieri, Enzo
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2012, 17 (9-10) : 935 - 1000
  • [38] A PRIORI ESTIMATES AND MULTIPLICITY FOR SYSTEMS OF ELLIPTIC PDE WITH NATURAL GRADIENT GROWTH
    Nornberg, Gabrielle
    Schiera, Delia
    Sirakov, Boyan
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (06) : 3857 - 3881
  • [39] Nonexistence results for elliptic equations with gradient terms
    Alarcon, S.
    Burgos-Perez, M. A.
    Garcia-Melian, J.
    Quaas, A.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (01) : 758 - 780
  • [40] Gradient potential estimates for elliptic obstacle problems
    Xiong, Qi
    Zhang, Zhenqiu
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 495 (01)
12345