| Abstract: |
| In this talk,, we introduce two novel classes of quasilinear elliptic equations, each driven by the double phase
operator with variable exponents. The first class features a new double phase equation where exponents depend on the gradient
of the solution. In the second category,
the treatment of exponents is dependent on the solution itself. This class differs from the first one due to the unavailability of
suitable Musielak-Orlicz Sobolev spaces. For this reason, we employ a perturbation argument that leads to the classical double
phase class. |
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