| Abstract: |
| In this talk, we discuss recent regularity results for parabolic double-phase equations and systems, focusing on Lipschitz regularity in the presence of gradient nonlinearities. Our approach is based on the celebrated Ishii-Lions method for viscosity solutions. We show that when the modulating coefficient is spatially Lipschitz and its zero set satisfies a mild and natural control condition, then bounded weak solutions to parabolic double-phase equations with gradient nonlinearity are locally Lipschitz continuous in space and 1/2 H\{o}lder continuous in time. Furthermore, we also discuss the higher integrability result for parabolic double phase systems having two modulating coefficients. |
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