Functions continuous in the fine topology for the heat equation
Functions of finite fractional variation and their applications to fractional impulsive equations
We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a -additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures.
Functions of four variables which satisfy both the heat equation and the Laplace equation in three variables - II
Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains
We introduce a sort of "local" Morrey spaces and show an existence and uniqueness theorem for the Dirichlet problem in unbounded domains for linear second order elliptic partial differential equations with principal coefficients "close" to functions having derivatives in such spaces.
Fundamental decay mode and asymptotic behaviour of positive semigroups
Fundamental inequalities on firmly stratified sets and some applications.
Fundamental operator-functions of degenerate differential and difference-differential operators in Banach spaces which have a Noether operator in the principal part.
Fundamental operator-valued functions of singular differential operators in Banach spaces.
Fundamental solution of the operator for n>3
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 for operators preserving a quadratic form
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 . I. Fundamental Solutions.
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 Dirac-type operators
We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces and . Further, we consider the Cauchy problem for this operator.
Fundamental solutions for translation and rotation invariant differential operators on the Heisenberg group
Fundamental solutions of pseudo-differential operators over -adic fields
Fundamental solutions of the differential operator