An Intrinsic Sobolev Trace Theory for Riemannian Vector Bundles with Applications to Quasilinear Elliptic Equations

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 \(m\ge1\)