We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique W^{1,1}_0 distributional solution under suitable summability assumptions on the source in Lebesgue spaces. Moreover, we prove tha
t our problem has no solution if the source is a Radon measure concentrated on a set of zero harmonic capacity.
We consider a boundary value problem in a bounded domain involving a degenerate operator of the form $$L(u)=-textrm{div} (a(x) abla u)$$ and a suitable nonlinearity $f$. The function $a$ vanishes on smooth 1-codimensional submanifolds of $Omega$ wher
e it is not allowed to be $C^{2}$. By using weighted Sobolev spaces we are still able to find existence of solutions which vanish, in the trace sense, on the set where $a$ vanishes.
Lucio Boccardo
,Gisella Croce
.
(2013)
.
"$W^{1,1}_0(Omega)$ in some borderline cases of elliptic equations with degenerate coercivity"
.
Gisella Croce
هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا