A singular elliptic equation with natural growth in the gradient and a variable exponent
Ficheros
Identificadores
URI: http://hdl.handle.net/10835/15696
DOI: https://doi.org/10.1007/s00030-015-0351-0
DOI: https://doi.org/10.1007/s00030-015-0351-0
Compartir
Metadatos
Mostrar el registro completo del ítemFecha
2015Resumen
In this paper we consider singular quasilinear elliptic equations with quadratic gradient and a singular term with a variable exponent
−∆u +
|∇u|
2
uγ(x) = f in Ω,
u = 0 on ∂Ω.
Here Ω is an open bounded set of R
N , γ(x) is a positive continuous
function and f is positive function that belongs to a certain Lebesgue
space.
We show, among other results, that there exists a solution in the
natural energy space H1
0 (Ω) to this problem when γ(x) is strictly less
than 2 in a strip around the boundary; while there is no solution in
the energy space when there exists Γ ⊂ ∂Ω with |Γ|N−1 > 0 such that
γ(x) > 2 on Γ.
Moreover, since we work by approximation we can analyze the behavior of the approximated solutions un in the case in which there is no
solution in H1
0 (Ω).
Palabra/s clave
Nonlinear elliptic equations
Singular natural growth gradient terms
Positive solutions
Variable exponent