Remark on some non-uniformly nonlinear elliptic equations
Keywords:
Nonlinear elliptic equations, Degenerate coercivity, Regularity, A priori estimates, RearrangementAbstract
We consider the Dirichlet problem for a class of nonlinear elliptic equations with degenerate coercivity whose model is
$$ {\rm div}\left(\displaystyle{\frac{|\nabla
u|^{p-2}{\nabla}u}{(1+|u|)^{\theta(p-1)}}}\right)={\rm div}F, $$
with 0 < θ < 1 and |F| ∈ Ls (Ω). When θ is sufficiently close to 1, we prove that the solutions are not in Sobolev spaces.
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