What are the eigenvalues and eigenfunctions of the Euclidean Laplacian for the annulus in 2D bound by radii r_1 < 1 < r_2 if we consider zero Dirichlet boundary conditions? I’m aware that this is something to derive by separation of variables in polar coordinates but I would very much appreciate a reference or suggestions!
2026-03-25 17:22:43.1774459363
Dirichlet Spectrum of Laplacian In 2D Annulus
124 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in SPECTRAL-THEORY
- Why is $\lambda\mapsto(\lambda\textbf{1}-T)^{-1}$ analytic on $\rho(T)$?
- Power spectrum of field over an arbitrarily-shaped country
- Calculating spectrum and resolvent set of a linear operator (General question).
- Operator with compact resolvent
- bounded below operator/ Kato-Rellich
- Show directly that if $E_1\geqslant E_2\geqslant\dots$, then $E_i\rightarrow \bigwedge E_i$ strongly.
- Is the spectral radius less than $1$?
- How to show range of a projection is an eigenspace.
- Spectral radius inequality for non-abelian Banach algebras
- Do unitarily equivalent operators have the same spectrum?
Related Questions in LAPLACIAN
- Polar Brownian motion not recovering polar Laplacian?
- Trivial demonstration. $\nabla J(r,t)=\frac{\hbar}{im}\nabla\psi^{*}\nabla\psi+\frac{\hbar}{im}\psi\nabla^2\psi$
- Bochner nonnegativity theorem for Laplace-Beltrami eigenfunctions?
- Physicists construct their potentials starting from the Laplace equation, why they do not use another differential operator, like theta Θ?
- Integral of the Laplacian of a function that is constant on the sphere
- Trying to show 9 point laplacian equivalence
- Does the laplacian operator work on time as well as spacial variables?
- Find the Green's function $G(\mathbf{x},\xi)$, such that $\nabla^2G = \delta(\mathbf{x}-\xi)$
- Laplace-Beltrami operator in $\mathbb{R}^m$
- demonstration of vector laplacian in cartesian coordinates
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?