An Existence Result Via L s Regularity for Some Nonlinear Elliptic Equations

1992 ◽  
pp. 145-152
Author(s):  
Lucio Boccardo ◽  
François Murat
Keyword(s):  
Elliptic Equations ◽  
Existence Result ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

scholarly journals Existence of Solution for Nonlinear Elliptic Equations with Unbounded Coefficients and Data

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Hicham Redwane
Keyword(s):  
Elliptic Equations ◽  
Existence Result ◽  
Nonlinear Elliptic Equations ◽  
Existence Of Solution ◽  
Unbounded Coefficients ◽  
Renormalized Solution ◽  
Nonlinear Elliptic

An existence result of a renormalized solution for a class of nonlinear elliptic equations is established. The diffusion functions may not be in for a finite value of the unknown and the data belong to .

scholarly journals Existence results for a perturbed Dirichlet problem without sign condition in Orlicz spaces

2020 ◽  
Vol 72 (4) ◽  
pp. 509-526
Author(s):  
H. Moussa ◽  
M. Rhoudaf ◽  
H. Sabiki
Keyword(s):  
Elliptic Equations ◽  
Existence Result ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Nonlinear Elliptic ◽  
Sign Condition ◽  
Carathéodory Function ◽  
Monotone Vector Field ◽  
The Right

UDC 517.5 We deal with the existence result for nonlinear elliptic equations related to the form < b r > A u + g ( x , u , ∇ u ) = f , < b r > where the term - ⅆ i v ( a ( x , u , ∇ u ) ) is a Leray–Lions operator from a subset of W 0 1 L M ( Ω ) into its dual.  The growth and coercivity conditions on the monotone vector field a are prescribed by an N -function M which does not have to satisfy a Δ 2 -condition. Therefore we use Orlicz–Sobolev spaces which are not necessarily reflexive and assume that the nonlinearity g ( x , u , ∇ u ) is a Carathéodory function satisfying only a growth condition with no sign condition. The right-hand side~ f belongs to W -1 E M ¯ ( Ω ) .

A new concept of reduced measure for nonlinear elliptic equations

2004 ◽  
Vol 339 (3) ◽  
pp. 169-174 ◽  
Author(s):  
Haïm Brezis ◽  
Moshe Marcus ◽  
Augusto C. Ponce
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates

2019 ◽  
Vol 21 (07) ◽  
pp. 1850053 ◽  
Author(s):  
J. V. da Silva ◽  
G. C. Ricarte
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
Integrability Condition ◽  
A Priori ◽  
Nonlinear Elliptic Equations ◽  
Borderline Case ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Text Type ◽  
Nonlinear Elliptic

In this paper, we establish global Sobolev a priori estimates for [Formula: see text]-viscosity solutions of fully nonlinear elliptic equations as follows: [Formula: see text] by considering minimal integrability condition on the data, i.e. [Formula: see text] for [Formula: see text] and a regular domain [Formula: see text], and relaxed structural assumptions (weaker than convexity) on the governing operator. Our approach makes use of techniques from geometric tangential analysis, which consists in transporting “fine” regularity estimates from a limiting operator, the Recession profile, associated to [Formula: see text] to the original operator via compactness methods. We devote special attention to the borderline case, i.e. when [Formula: see text]. In such a scenery, we show that solutions admit [Formula: see text] type estimates for their second derivatives.

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