Friday, February 21, 2020 - 15:15 in D5-153
Calderón-Zygmund Estimates for Elliptic Double Phase Problems with Variable Exponents
A talk in the Oberseminar Analysis series by
Ho-Sik Lee
| Abstract: |
As an issue of regularity of PDE, we study an operator of the type,
which is called elliptic double phase problems with variable exponents.
We obtained Calderón-Zygmund estimates for the problem, under minimal
regularity requirements on the nonlinearities. The problem under
consideration is
div $(|Du|^{p(x)-2} Du + a(x)|Du|^{q(x)-2} Du)$
= div $ (|F|^{p(x)-2}F + a(x)|F|^{q(x)-2}F) $
in an open bounded subset $\Omega$ of $\mathbb{R}^n$, $n \ge 2$, where $a(x)$ is Hölder continuous
and variable exponent functions $p(x)$ and $q(x)$ have the modulus of
continuity $\omega(\cdot)$:
$|p(x) - p(y)| + |q(x) - q(y)| \le \omega(|x - y|)$
|
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