| 구분 |
학생(팀) 세미나 |
| 일정 |
2017-02-08 13:00 ~ 15:00 |
| 강연자 |
|
| 기타 |
|
| 담당교수 |
*연구원 |
In this talk, we consider elliptic equations of the following type
$$
-mathrm{div},left(a(x)|Du|^{p-2}Du
ight)+ V|u|^{p-2}u=-mathrm{div},left(|F|^{p-2}F
ight) ext{in} Omega, u=0 ext{on} partialOmega.
$$
Here $V$ is nonnegative function. For $gamma>frac{n}{p}$, we prove that if $Vin L^q(Omega)$ satisfies the reverse H"older inequality that
$$
left(frac{1}{|B|}int_BV^{gamma}dx
ight)^{frac{1}{gamma}}leq cfrac{1}{|B|}int_BVdx
$$
for all balls $B$ and for some constant $c>0$, then the following implication holds
$$
Fin L^q(Omega) Longrightarrow Fin L^q(Omega)
$$
for every $qleq gamma^*(p-1)$ with $gamma^*:=frac{ngamma}{n-gamma}$, under possibly minimal assumptions on coefficients and domains.
