Ellipticity and invertibility in the cone algebra onLp-Sobolev spaces

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Existence and maximal Lp-regularity of solutions for the porous medium equation on manifolds with conical singularities (2015, background): “5 in [25] that the kernel and the cokernel are independent of s and p, we find that it is also invertible for s < 0.”
Cone Sobolev inequality and Dirichlet problem for nonlinear elliptic equations on a manifold with conical singularities (2012, unknown): “[11]) We have H p (X∧) ⊂ W m,p loc (X∧) for all m ∈ N, γ ∈ R, where W m,p loc (X ∧) denotes the subspace of all u ∈ D′(X∧) such that φu ∈ W m,p(X∧) for every φ ∈ C∞ 0 (X∧).”
Existence theorem for a class of semilinear totally characteristic elliptic equations with critical cone Sobolev exponents (2011, result): “Our study is in fact motivated by the study of Schrohe and Seiler in [ 10 ].”
Global existence and nonexistence for semilinear parabolic equations with conical degeneration (2012, background): “Recently, the authors in [1] introduced a class of weighted Sobolev spaces (also see [3,10,11]), and proved the corresponding cone Sobolev inequality and Poincaré inequality.”