This monograph develops an introduction to global analysis centered on the interaction between differential geometry, functional analysis, partial differential equations, and variational methods on Riemannian manifolds. Beginning with smooth and Riemannian geometry, it develops Sobolev spaces, distributions, interpolat...
Carlos D. Velázquez-Mendoza, María de los Ángeles Sandoval-Romero, R. Carlos· 0 citations
This monograph develops an introduction to global analysis centered on the interaction between differential geometry, functional analysis, partial differential equations, and variational methods on Riemannian manifolds. Beginning with smooth and Riemannian geometry, it develops Sobolev spaces, distributions, interpolat...
Carlos D. Velázquez-Mendoza, María de los Ángeles Sandoval-Romero, R. Carlos· 0 citations
Let \(\mathbf{E}\to M\) be a finite-rank Riemannian vector bundle over a compact Riemannian manifold with nonempty smooth boundary, equipped with a compatible connection. We develop an intrinsic trace theory for Sobolev sections defined through weak covariant derivatives. For every integer \(m\ge1\) and every \(1\le p<...
Carlos D. Velázquez-Mendoza, María de los Ángeles Sandoval-Romero, R. Carlos· 0 citations
We study Kirchhoff-Boussinesq-type equations on closed Riemannian manifolds $(M,g)$ of the form \[ \sum_{j=0}^m a_i(-\Delta_g)^m u \pm \text{div}_g(\vert\nabla u\vert_g^{p-2}\nabla u) = f(u),\qquad \text{ on }\ M, \] where $m<\dim M/2$, $(a_0,a_1,\ldots a_m)\in C^\infty_+(M)\times [0,\infty)^{m-1}\times(0,\infty)$, $2<...
R. Carlos, Juan Carlos Fernandez, María de los Ángeles Sandoval-Romero· 0 citations
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