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Volume 27, Issue 1
L1 Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent

Stanislas Ouaro & Arouna Ouedraogo

DOI: 10.4208/jpde.v27.n1.1

J. Part. Diff. Eq., 27 (2014), pp. 1-27.

Published online: 2014-03

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  • Abstract

In this work, we study the following nonlinear homogeneous Neumann boundary value problem $β(u)−diva(x,∇u) ∋ f in Ω, a(x,∇u)⋅η$ $=0$ on $∂Ω$, where $Ω$ is a smooth bounded open domain in $ℜ^N, N ≥ 3$ with smooth boundary $∂Ω$ and $η$ the outer unit normal vector on $∂Ω$. We prove the existence and uniqueness of an entropy solution for L¹-data f. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.

  • Keywords

Elliptic equation variable exponent entropy solution L¹-data Neumann boundary condition

  • AMS Subject Headings

35K55, 35D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ouaro@yahoo.fr (Stanislas Ouaro)

arounaoued2002@yahoo.fr (Arouna Ouedraogo)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-27-1, author = {Ouaro , Stanislas and Ouedraogo , Arouna}, title = {L1 Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent}, journal = {Journal of Partial Differential Equations}, year = {2014}, volume = {27}, number = {1}, pages = {1--27}, abstract = {

In this work, we study the following nonlinear homogeneous Neumann boundary value problem $β(u)−diva(x,∇u) ∋ f in Ω, a(x,∇u)⋅η$ $=0$ on $∂Ω$, where $Ω$ is a smooth bounded open domain in $ℜ^N, N ≥ 3$ with smooth boundary $∂Ω$ and $η$ the outer unit normal vector on $∂Ω$. We prove the existence and uniqueness of an entropy solution for L¹-data f. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n1.1}, url = {http://global-sci.org/intro/article_detail/jpde/5123.html} }
TY - JOUR T1 - L1 Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent AU - Ouaro , Stanislas AU - Ouedraogo , Arouna JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 27 PY - 2014 DA - 2014/03 SN - 27 DO - http://doi.org/10.4208/jpde.v27.n1.1 UR - https://global-sci.org/intro/article_detail/jpde/5123.html KW - Elliptic equation KW - variable exponent KW - entropy solution KW - L¹-data KW - Neumann boundary condition AB -

In this work, we study the following nonlinear homogeneous Neumann boundary value problem $β(u)−diva(x,∇u) ∋ f in Ω, a(x,∇u)⋅η$ $=0$ on $∂Ω$, where $Ω$ is a smooth bounded open domain in $ℜ^N, N ≥ 3$ with smooth boundary $∂Ω$ and $η$ the outer unit normal vector on $∂Ω$. We prove the existence and uniqueness of an entropy solution for L¹-data f. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.

Stanislas Ouaro & Arouna Ouedraogo. (2019). L1 Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent. Journal of Partial Differential Equations. 27 (1). 1-27. doi:10.4208/jpde.v27.n1.1
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