Mukhtar Karazym, Durvudkhan Suragan
Published 2023-06-26Version 1
Based on variational methods, we study a nonlinear eigenvalue problem for a $p$-sub-Laplacian type quasilinear operator arising from smooth H\"ormander vector fields. We derive the smallest eigenvalue, prove its simplicity and isolatedness, establish the positivity of the first eigenfunction and show H\"older regularity of eigenfunctions. Moreover, we determine the best constant for the $L^{p}$-Poincar\'e inequality as a byproduct.
Bounds for the extremal parameter of nonlinear eigenvalue problems and application to the explosion problem in a flow
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