We present results in [11, 12] for viscosity solutions to a one-phase free boundary problem for the p(x)- Laplacian with non-zero right hand side. We prove that viscosity solutions are locally Lipschitz continuous, which is the optimal regularity. Then we prove that flat and Lipschitz free boundaries of viscosity solutions are C1,. We also introduce some applications and moreover, we obtain new results for the operator considered.We present results in [11, 12] for viscosity solutions to a one-phase free boundary problem for the p(x)-Laplacian with non-zero right hand side. We prove that viscosity solutions are locally Lipschitz continuous, which is the optimal regularity. Then we prove that flat and Lipschitz free boundaries of viscosity solutions are C¹. We also introduce some applications and moreover, we obtain new results for the operator considered.
Ferrari, F., Lederman, C. (2023). FREE BOUNDARY REGULARITY FOR A ONE-PHASE PROBLEM WITH NON-STANDARD GROWTH.
FREE BOUNDARY REGULARITY FOR A ONE-PHASE PROBLEM WITH NON-STANDARD GROWTH
F. Ferrari;
2023
Abstract
We present results in [11, 12] for viscosity solutions to a one-phase free boundary problem for the p(x)- Laplacian with non-zero right hand side. We prove that viscosity solutions are locally Lipschitz continuous, which is the optimal regularity. Then we prove that flat and Lipschitz free boundaries of viscosity solutions are C1, . We also introduce some applications and moreover, we obtain new results for the operator considered.We present results in [11, 12] for viscosity solutions to a one-phase free boundary problem for the p(x)-Laplacian with non-zero right hand side. We prove that viscosity solutions are locally Lipschitz continuous, which is the optimal regularity. Then we prove that flat and Lipschitz free boundaries of viscosity solutions are C¹. We also introduce some applications and moreover, we obtain new results for the operator considered.| File | Dimensione | Formato | |
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