Nonlinear elliptic equations, rearrangements of functions and orlicz spaces

1979 ◽  
Vol 120 (1) ◽  
pp. 159-184 ◽  
Author(s):  
Giorgio Talenti
Keyword(s):  
Elliptic Equations ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

Weighted Orlicz regularity estimates for fully nonlinear elliptic equations with asymptotic convexity

2019 ◽  
Vol 21 (04) ◽  
pp. 1850024 ◽  
Author(s):  
Mikyoung Lee
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Operator ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Regularity Estimates ◽  
Hessian Estimates ◽  
Asymptotic Convexity

We prove interior Hessian estimates in the setting of weighted Orlicz spaces for viscosity solutions of fully nonlinear, uniformly elliptic equations [Formula: see text] under asymptotic assumptions on the nonlinear operator [Formula: see text] The results are further extended to fully nonlinear, asymptotically elliptic equations.

scholarly journals Existence of a weak bounded solution for nonlinear degenerate elliptic equations in Musielak-Orlicz spaces

2020 ◽  
Vol 6 (1) ◽  
pp. 16-33 ◽  
Author(s):  
M. Bourahma ◽  
J. Bennouna ◽  
M. El Moumni
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Bounded Solution ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

AbstractIn this paper, we show the existence of solutions for the nonlinear elliptic equations of the form\left\{ {\matrix{ { - {\rm{div}}\,a\left( {x,u,\nabla u} \right) = f,} \hfill \cr {u \in W_0^1L\varphi \left( \Omega \right) \cap {L^\infty }\left( \Omega \right),} \hfill \cr } } \right.where a\left( {x,s,\xi } \right) \cdot \xi \ge \bar \varphi _x^{ - 1}\left( {\varphi \left( {x,h\left( {\left| s \right|} \right)} \right)} \right)\varphi \left( {x,\left| \xi \right|} \right) and h : ℝ+→]0, 1] is a continuous decreasing function with unbounded primitive. The second term f belongs to LN(Ω) or to Lm(Ω), with m = {{rN} \over {r + 1}} for some r > 0 and φ is a Musielak function satisfying the Δ2-condition.

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 ) .

Existence of renormalized solutions for some strongly nonlinear elliptic equations in Orlicz spaces

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Azeddine Aissaoui Fqayeh ◽  
Abdelmoujib Benkirane ◽  
Mostafa El Moumni ◽  
Ahmed Youssfi
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Renormalized Solutions ◽  
Renormalized Solution ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic

AbstractWe prove the existence of a renormalized solution for the Dirichlet problem associated to the nonlinear elliptic equations div

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