Geometric estimates of solutions of quasilinear elliptic inequalities

2020 ◽  
Vol 84 (6) ◽  
pp. 1056-1104
Author(s):  
A. A. Kon’kov
Keyword(s):  
Estimates Of Solutions ◽  
Quasilinear Elliptic ◽  
Geometric Estimates ◽  
Elliptic Inequalities

Behavior of solutions of quasilinear elliptic inequalities in an unbounded domain

1996 ◽  
Vol 60 (4) ◽  
pp. 415-424
Author(s):  
A. B. Shapoval
Keyword(s):  
Unbounded Domain ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities

scholarly journals Quasilinear elliptic inequalities with Hardy potential and nonlocal terms

2020 ◽  
pp. 1-19
Author(s):  
Marius Ghergu ◽  
Paschalis Karageorgis ◽  
Gurpreet Singh
Keyword(s):  
Riesz Potential ◽  
Sufficient Conditions ◽  
Hardy Potential ◽  
Existence Of Positive Solutions ◽  
Elliptic Inequality ◽  
Image Position ◽  
Nonlocal Terms ◽  
Necessary And Sufficient ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities

We study the quasilinear elliptic inequality \[ -\Delta_m u - \frac{\mu}{|x|^m}u^{m-1} \geq (I_\alpha*u^p)u^q \quad\mbox{in }\mathbb{R}^N\setminus \overline B_1, N\geq 1, \] where $p>0$ , $q, \mu \in \mathbb {R}$ , $m>1$ and $I_\alpha$ is the Riesz potential of order $\alpha \in (0,N)$ . We obtain necessary and sufficient conditions for the existence of positive solutions.

scholarly journals Quasilinear elliptic inequalities on complete Riemannian manifolds

2007 ◽  
Vol 87 (6) ◽  
pp. 582-600 ◽  
Author(s):  
Paolo Antonini ◽  
Dimitri Mugnai ◽  
Patrizia Pucci
Keyword(s):  
Riemannian Manifolds ◽  
Complete Riemannian Manifolds ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities

Behavior of solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives

1998 ◽  
Vol 64 (6) ◽  
pp. 817-821
Author(s):  
A. A. Kon'kov
Keyword(s):  
Lower Order ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities

scholarly journals Quasilinear elliptic equations with sub-natural growth and nonlinar potentials

2015 ◽  
Author(s):  
◽  
Dat Tien Cao
Keyword(s):  
Sufficient Conditions ◽  
Finite Energy ◽  
Quasilinear Elliptic Equations ◽  
Natural Growth ◽  
Estimates Of Solutions ◽  
Regularity Properties ◽  
Nonlinear Potentials ◽  
Necessary And Sufficient ◽  
Quasilinear Elliptic

Necessary and sufficient conditions for the existence of finite energy and weak solutions are given. Sharp global pointwise estimates of solutions are obtained as well. We also discuss the uniqueness and regularity properties of solutions. As a consequence, characterization of solvability of the equations with singular natural growth in the gradient terms is deduced. Our main tools are Wolff potential estimates, dyadic models, and related integral inequalities. Special nonlinear potentials of Wolff type ssociated with "sublinear" problems are constructed to obtain sharp bounds of solutions. We also treat equations with the fractional Laplacians. Our approach is applicable to more general quasilinear A-Laplace operators as well as the fully nonlinear k-Hessian operators.

scholarly journals On solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives

2013 ◽  
Vol 90 ◽  
pp. 121-134 ◽  
Author(s):  
Andrej A. Kon’kov
Keyword(s):  
Lower Order ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities
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