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It is shown that the partial differential operator $P (D) = \partial ⁴ / \partial x ⁴ - \partial ² / \partial y ² + i \partial / \partial z : Γ^{d} (ℝ ³) \to Γ^{d} (ℝ ³)$ is surjective if 1 ≤ d < 2 or d ≥ 6 and not surjective for 2 ≤ d < 6.

A posteriori estimations of approximate solutions for some types of boundary value problems

Kodnár, Rudolf (1986)

Equadiff 6

A priori estimates for higher order hyperbolic equations.

Mitsuru Sugimoto (1994)

Mathematische Zeitschrift

A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence

Oleg Morozov (2014)

Open Mathematics

We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.

A symmetrization result for elliptic equations with lower-order terms

Guido Trombetti, Juan Luis Vazquez (1985)

Annales de la Faculté des sciences de Toulouse : Mathématiques

A symmetrization result for nonlinear elliptic equations.

Vincenzo Ferone, Basilio Messano (2004)

Revista Matemática Complutense

We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = g(x,u) + f, where the principal term is a Leray-Lions operator defined on W01,p (Ω). The function g(x,u) satisfies suitable growth assumptions, but no sign hypothesis on it is assumed. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.

A Two-Particle Quantum System with Zero-Range Interaction

Michele Correggi (2008/2009)

Séminaire Équations aux dérivées partielles

We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.

Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.

Muro, Masakazu (2004)

Journal of Lie Theory

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A Cauchy problem for $u_{t} - Δ u = u^{p} with 0 < p < 1$ . Asymptotic behaviour of solutions

A class of pseudo differential operators with multiple non-involutive characteristics

A field equation defined by a Hurwitz pair

A general controllability theorem

A Geometric Intrepertation for the Hans Lewy Operator

A geometrical interpretation of the time evolution of the Schrödinger equation for discrete quantum systems

A note on the Dirichlet problem for the elliptic linear operator in Sobolev spaces with weight $d_{M}^{ϵ}$

A partial differential operator which is surjective on Gevrey classes $Γ^{d} (ℝ ³)$ with 1 ≤ d < 2 and d ≥ 6 but not for 2 ≤ d < 6

A posteriori estimations of approximate solutions for some types of boundary value problems

A priori estimates for higher order hyperbolic equations.

A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence

A symmetrization result for elliptic equations with lower-order terms

A symmetrization result for nonlinear elliptic equations.

A Two-Particle Quantum System with Zero-Range Interaction

Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.

Almost product structures and Monge-Ampère equations.

An estimate of the gap of the first two eigenvalues in the Schrödinger operator

Analytic and Gevrey Hypoellipticity

Applications of symmetry methods to the theory of plasma physics.

Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.

Currently displaying 1 – 20 of 221