# Linear PDE with Constant Coefficients

@article{Manssour2021LinearPW, title={Linear PDE with Constant Coefficients}, author={Rida Ait El Manssour and Marc H{\"a}rk{\"o}nen and Bernd Sturmfels}, journal={ArXiv}, year={2021}, volume={abs/2104.10146} }

We discuss practical methods for computing the space of solutions to an arbitrary homogeneous linear system of partial differential equations with constant coefficients. These rest on the Fundamental Principle of Ehrenpreis–Palamodov from the 1960s. We develop this further using recent advances in computational commutative algebra.

## 6 Citations

### Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients

- Computer ScienceArXiv
- 2022

The Ehrenpreis-Palamodov fundamental principle is applied, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs, and can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise deﬁned initial and boundary conditions.

### Primary Decomposition with Differential Operators

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We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by differential conditions. The minimal number of conditions needed is the…

### An elementary approach to the homological properties of constant-rank operators

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. We give a simple and constructive extension of Rait , ˘a’s result that every constant-rank operator possesses an exact potential and an exact annihilator. Our construction is completely…

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We study commutative algebras with Gorenstein duality, i.e. algebras A equipped with a nondegenerate bilinear pairing such that 〈ac, b〉 = 〈a, bc〉 for any a, b, c ∈ A. If an algebra A is Artinian,…

### Oscillation and Concentration in Sequences of PDE Constrained Measures

- MathematicsArchive for Rational Mechanics and Analysis
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We show that for constant rank partial differential operators A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

### Syzygies, constant rank, and beyond

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- 2021

We study linear PDE with constant coefficients. The constant rank condition on a system of linear PDEs with constant coefficients is often used in the theory of compensated compactness. While this is…

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