| 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. |
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