Boundedness of the extremal solution for some $p$-Laplacian problems

Year, pages: 2014, 379 - 390

We investigate the regularity of extremal solutions to some $p$-Laplacian Dirichlet problems with strong nonlinearities. Under adequate assumptions we prove the smoothness of the extremal solutions for some classes of nonlinearities. Our results suggest that the extremal solution's boundedness for some range of dimensions depends on the nonlinearity $f$.

Wei, L. 2014. Boundedness of the extremal solution for some $p$-Laplacian problems. In Mathematica Slovaca, vol. 64, no.2, pp. 379-390. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0211-0

Wei, L. (2014). Boundedness of the extremal solution for some $p$-Laplacian problems. Mathematica Slovaca, 64(2), 379-390. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0211-0