Related papers: On Analytic Solvability and Hypoellipticity For $\…
This is a reaction to the article Symplectic bipotentials, in published form [2] Harakeh M, Ban M, de Saxce G. Symplectic bipotentials. Mathematics and Mechanics of Solids. 2026;0(0) doi:10.1177/10812865251413554, and in preprint form [1]…
This note is withdrawn. The result and its proof are available in the literature.
In this paper we study existence and nonexistence of nonnegative distributional solutions for a class of semilinear fractional elliptic equations involving the Hardy potential.
We study some size estimates for the solution of the equation d-bar u=f in one variable. The new ingredient is the use of holomorphic functions with precise growth restrictions in the construction of explicit solutions to the equation.
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Let A be an idempotent algebra on a 3-element domain D that omits a G-set for a factor. Suppose A is not \alpha\beta-projective (for some alpha, beta subsets of D) and is not collapsible. It follows that A is switchable. We prove that, for…
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
The solvability in Sobolev spaces $W^{1,2}_p$ is proved for nondivergence form second order parabolic equations for $p>2$ close to 2. The leading coefficients are assumed to be measurable in the time variable and two coordinates of space…
An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct analytical potential-density pairs of infinitesimally…
An integral solution operator for $\bar\partial$ is constructed on product domains that include the punctured bidisc. This operator is shown to satisfy $L^p$ estimates for all $1\leq p <\infty$, though with non-standard -- relative to…
We present a construction of the explicit Hodge decomposition for $\bar\partial$-equation on Riemann surfaces.
Certain second-order partial differential operators, which are expressed as sums of squares of real-analytic vector fields in $\Bbb R^3$ and which are well known to be $C^\infty$ hypoelliptic, fail to be analytic hypoelliptic.
The CR manifold M_m = { Im z_2= Re z_1^{2m} } (m=2,3,...) is the counterexample, which has been given by M. Christ and D. Geller, to analytic hypoellipticity of d-bar-b and real analyticity of the Szego kernel. In order to give a direct…
We present a result about solvability in $W^{2}_{p}$, $p>d$, in the whole space $\bR^{d}$ of Bellman's equations with VMO ``coefficients''. Parabolic equations are touched upon as well.
In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations in a complex Hilbert space. We are able to decompose the unit square of the parameters into three parts where the…
We prove several general results on non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point.
Let Y be a weighted homogeneous (singular) subvariety of C^n. The main objective of this paper is to present a class of explicit integral formulae for solving the d-bar-equation $\omega=\dbar\lambda$ on the regular part of Y, where $\omega$…
This article presents a new approach of semigroup analysis and pseudo-differential calculus for deriving the regularizing estimate on non-cutoff linearized Boltzmann equation. We are able to obtain regularizing estimate of semigroup…
We are concerned with the problem of real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata…
We extend several known results on solvability in the Sobolev spaces $W^{1}_{p}$, $p\in[2,\infty)$, of SPDEs in divergence form in $\bR^{d}_{+}$ to equations having coefficients which are discontinuous in the space variable.