Special Session 5: Recent results in Nonlinear PDEs

Existence and regularity results for a class of parabolic problems with double phase flux of variable growth

Rakesh Arora
Indian Institute of Technology, Varanasi, India
India
Co-Author(s):    Sergey Shmarev
Abstract:
This talk presents existence and regularity results for a class of double-phase parabolic problems with homogeneous Dirichlet boundary conditions. We find conditions on the source term and the initial data that guarantee the existence of a unique strong solution $u$. The solution possesses the property of global higher integrability of the gradient which is derived with the help of new interpolation inequalities in the variable Sobolev spaces. The second-order differentiability of the strong solution is also proven.