scholarly journals Oblique derivative problem for quasilinear elliptic equations with VMO coefficients

1996 ◽  
Vol 53 (3) ◽  
pp. 501-513 ◽  
Author(s):  
Guiseppe Di Fazio ◽  
Dian K. Palagachev
Keyword(s):  
Sobolev Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Oblique Derivative Problem ◽  
Strong Solvability ◽  
Derivative Problem ◽  
Carathéodory Functions ◽  
Vmo Coefficients ◽  
Image Position ◽  
Quasilinear Elliptic

Strong solvability and uniqueness in the Sobolev space W2, q(Ω), q > n, are proved for the oblique derivative problemassuming the coefficients of the quasilinear elliptic operator to be Carathéodory functions, aij ∈ VMO∩L∞ with respect to x, and b to grow at most quadratically with respect to the gradient.

Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media

2006 ◽  
Vol 136 (6) ◽  
pp. 1131-1155 ◽  
Author(s):  
B. Amaziane ◽  
L. Pankratov ◽  
A. Piatnitski
Keyword(s):  
Elliptic Equation ◽  
Asymptotic Behaviour ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Quasilinear Equation ◽  
Quasilinear Elliptic Equations ◽  
High Contrast ◽  
Small Measure ◽  
Image Position ◽  
Quasilinear Elliptic

The aim of the paper is to study the asymptotic behaviour of the solution of a quasilinear elliptic equation of the form with a high-contrast discontinuous coefficient aε(x), where ε is the parameter characterizing the scale of the microstucture. The coefficient aε(x) is assumed to degenerate everywhere in the domain Ω except in a thin connected microstructure of asymptotically small measure. It is shown that the asymptotical behaviour of the solution uε as ε → 0 is described by a homogenized quasilinear equation with the coefficients calculated by local energetic characteristics of the domain Ω.

scholarly journals EXISTENCE OF POSITIVE EVANESCENT SOLUTIONS TO SOME QUASILINEAR ELLIPTIC EQUATIONS

2008 ◽  
Vol 78 (1) ◽  
pp. 157-162 ◽  
Author(s):  
OCTAVIAN G. MUSTAFA
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Elliptic Equations ◽  
Exterior Domain ◽  
Quasilinear Elliptic Equations ◽  
Image Position ◽  
Quasilinear Elliptic

AbstractWe establish that the elliptic equation defined in an exterior domain of ℝn, n≥3, has a positive solution which decays to 0 as $\vert x\vert \rightarrow +\infty $ under quite general assumptions upon f and g.

scholarly journals On the Harnack inequality for quasilinear elliptic equations with a first-order term

2018 ◽  
Vol 148 (5) ◽  
pp. 1075-1095 ◽  
Author(s):  
Susana Merchán ◽  
Luigi Montoro ◽  
Berardino Sciunzi
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Order Term ◽  
Quasilinear Elliptic Equations ◽  
First Order ◽  
Image Position ◽  
Quasilinear Elliptic ◽  
Comparison Inequality ◽  
Strong Comparison Principle ◽  
Iteration Technique

We consider weak solutions towith p > 1, q ≥ max{p − 1, 1}. We exploit the Moser iteration technique to prove a Harnack comparison inequality for C1 weak solutions. As a consequence we deduce a strong comparison principle.

Bifurcation for quasilinear elliptic equations on Rn with natural growth conditions

1989 ◽  
Vol 113 (3-4) ◽  
pp. 215-228 ◽  
Author(s):  
Cao Daomin ◽  
Li Gongbao ◽  
Yan Shusen
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Growth Conditions ◽  
Quasilinear Elliptic Equations ◽  
Natural Growth ◽  
Image Position ◽  
Quasilinear Elliptic

SynopsisWe consider the following eigenvalue problem:We prove the existence of H1(Rn)∩L∞(Rn) bifurcation at λ=0 but only require aij(x, t) (i,j= 1, 2, …,n) and f(x, t) to satisfy certain conditions in theneighbourhood of Rn × {0}.

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