Time fractional parabolic equations with partially SMO coefficients

H Dong, D Kim - Journal of Differential Equations, 2023 - Elsevier
We present the unique solvability in Sobolev spaces of time fractional parabolic equations in
divergence and non-divergence forms. The leading coefficients are merely measurable in (t …

Sobolev space theory for Poisson's and the heat equations in non-smooth domains via superharmonic functions and Hardy's inequality

J Seo - arXiv preprint arXiv:2304.10451, 2023 - arxiv.org
We prove the unique solvability for the Poisson and heat equations in non-smooth domains
$\Omega\subset\mathbb {R}^ d $ in weighted Sobolev spaces. The zero Dirichlet boundary …

The Cauchy problem for time-fractional linear nonlocal diffusion equations

S Wang, XF Zhou - Zeitschrift für angewandte Mathematik und Physik, 2023 - Springer
This manuscript is dedicated to study the Cauchy problem for time-fractional linear nonlocal
diffusion problems in the whole RN, including the existence and uniqueness of solutions …