Boundary blow-up for nonlinear elliptic equations with general growth in the gradient: an approach via symmetrisation
AbstractIn this paper we give a survey of some recent results obtained via symmetrization methods for solutions of elliptic equations in the form A(u) = H(x, u, Du), where the principal term is a laplacian-type operator and H(x, u, Du) grows with respect to Du at most like |Du|q , 1 ≤ q ≤ 2. In particular, it is considered the case where the solution blows up on the boundary and some comparison results are illustrated. Also an isoperimetric inequality for the so-called “ergodic constant” is given and the connections with the homogeneous Dirichlet problem for the quoted equations are discussed.
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.