Fundamental operator-functions of degenerate differential and difference-differential operators in Banach spaces which have a Noether operator in the principal part.
Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic operators with positive potentials
We show a weighted version of Fefferman-Phong's inequality and apply it to give an estimate of fundamental solutions, eigenvalue asymptotics and exponential decay of eigenfunctions for certain degenerate elliptic operators of second order with positive potentials.
Fundamental solution of initial-boundary value problem for fourth-order pseudoparabolic equations with nonsmooth coefficients.
Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.
We establish the uniqueness of fundamental solutions to the p-Laplacian equationut = div (|Du|p-2 Du), p > 2,defined for x ∈ RN, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equationut = ∆(um), m > 1,giving new and simpler proofs of known results. We finally introduce yet another method of proving asymptotic results based on the...
Fundamental Solutions and Eigenfunction Expansions for Schrödinger Operators. II. Eigenfunction Expansions.
Fundamental solutions and singular shocks in scalar conservation laws.
We study the existence and non-existence of fundamental solutions for the scalar conservation laws ut + f(u)x = 0, related to convexity assumptions on f. We also study the limits of those solutions as the initial mass goes to infinity. We especially prove the existence of so-called Friendly Giants and Infinite Shock Solutions according to the convexity of f, which generalize the explicit power case f(u) = um. We introduce an extended notion of solution and entropy criterion to allow infinite shocks...
Fundamental solutions for translation and rotation invariant differential operators on the Heisenberg group
Fundamental solutions of the differential operator