Potential estimates and local behavior of solutions to nonlinear elliptic equations and systems

We consider measure-data elliptic problems involving a second-order operator in a divergence form exhibiting Orlicz growth and having measurable coefficients. As known in the p-Laplace case, pointwise estimates for solutions expressed with the use of nonlinear potentials are powerful tools in the study of the local behavior of the solutions. Not only do we provide such estimates expressed in terms of such a potential, but also we investigate their regularity consequences. In particular, we show a sharp criterium for data that is equivalent to H\"older continuity of the solutions. The talk is based on joint works: (scalar) with F. Giannetti and A. Zatorska-Goldstein [arXiv:2006.02172] and (vectorial) with Y. Youn and A. Zatorska-Goldstein, [arXiv:2102.09313], [arXiv:2106.11639].

https://us02web.zoom.us/j/82881783943?pwd=TUp3OGNvZ3R5akpXclZESmx2aGVkUT09

Abstract: We consider measure-data elliptic problems involving a second-order operator in a divergence form exhibiting Orlicz growth and having measurable coefficients. As known in the p-Laplace case, pointwise estimates for solutions expressed with the use of nonlinear potentials are powerful tools in the study of the local behavior of the solutions. Not only do we provide such estimates expressed in terms of such a potential, but also we investigate their regularity consequences. In particular, we show a sharp criterium for data that is equivalent to H\"older continuity of the solutions. The talk is based on joint works: (scalar) with F. Giannetti and A. Zatorska-Goldstein [arXiv:2006.02172] and (vectorial) with Y. Youn and A. Zatorska-Goldstein, [arXiv:2102.09313], [arXiv:2106.11639].