scholarly journals Kato's inequalities for admissible functions to quasilinear elliptic operators A

2019 ◽  
Vol 51 (0) ◽  
pp. 49-64
Author(s):  
Xiaojing Liu ◽  
Toshio Horiuchi
Keyword(s):  
Elliptic Operators ◽  
Quasilinear Elliptic ◽  
Admissible Functions

scholarly journals ASYMPTOTIC BIFURCATION RESULTS FOR QUASILINEAR ELLIPTIC OPERATORS

2005 ◽  
Vol 47 (1) ◽  
pp. 55-67 ◽  
Author(s):  
JAN CHABROWSKI ◽  
PAVEL DRÁBEK ◽  
ELLIOT TONKES
Keyword(s):  
Elliptic Operators ◽  
Quasilinear Elliptic

scholarly journals On minimal decay at infinity of Hardy-weights

2019 ◽  
Vol 22 (05) ◽  
pp. 1950046 ◽  
Author(s):  
Hynek Kovařík ◽  
Yehuda Pinchover
Keyword(s):  
Elliptic Operators ◽  
Quasilinear Elliptic ◽  
Conditions At Infinity

We study the behavior of Hardy-weights for a class of variational quasilinear elliptic operators of [Formula: see text]-Laplacian type. In particular, we obtain necessary sharp decay conditions at infinity on the Hardy-weights in terms of their integrability with respect to certain integral weights. Some of the results are extended also to nonsymmetric linear elliptic operators. Applications to various examples are discussed as well.

Phragmen–Lindelöf theorems and the asymptotic behaviour of solutions of quasilinear elliptic equations in slabs

2000 ◽  
Vol 130 (2) ◽  
pp. 335-373 ◽  
Author(s):  
Z. Jin ◽  
K. Lancaster
Keyword(s):  
Asymptotic Behaviour ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Elliptic Operators ◽  
Dirichlet Boundary Conditions ◽  
Quasilinear Elliptic Equations ◽  
Compact Set ◽  
Asymptotic Behaviour Of Solutions ◽  
Quasilinear Elliptic ◽  
Dirichlet Boundary Data

The asymptotic behaviour of solutions of second-order quasilinear elliptic partial differential equations defined on unbounded domains in Rn contained in strips (when n = 2) or slabs (when n > 2) is investigated when such solutions satisfy Dirichlet boundary conditions and the Dirichlet boundary data have appropriate asymptotic behaviour at infinity. We prove Phragmèn–Lindelöf theorems for large classes of elliptic operators, including uniformly elliptic operators and operators with well-defined genre, establish exponential decay estimates for uniformly elliptic operators when the Dirichlet boundary data vanish outside a compact set, establish the uniqueness of solutions, and give examples of solutions for non-uniformly elliptic operators which decay but do not decay exponentially. Our principal theorems are proven using special barrier functions; these barriers are constructed by considering an operator associated to our original operator.

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