Does anyone know any reference that treats elliptic pdes with smooth variable coefficients (preferably on infinite domains, e.g, $\mathbb{R}^2$) and gives an estimate of the solution in terms of the norms of variable coefficients?
Thanks in advance
2026-03-26 01:28:48.1774488528
Estimates of solution of Elliptic PDE with variable coefficients
60 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in PARTIAL-DIFFERENTIAL-EQUATIONS
- PDE Separation of Variables Generality
- Partial Derivative vs Total Derivative: Function depending Implicitly and Explicitly on Variable
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Harmonic Functions are Analytic Evan’s Proof
- If $A$ generates the $C_0$-semigroup $\{T_t;t\ge0\}$, then $Au=f \Rightarrow u=-\int_0^\infty T_t f dt$?
- Regular surfaces with boundary and $C^1$ domains
- How might we express a second order PDE as a system of first order PDE's?
- Inhomogeneous biharmonic equation on $\mathbb{R}^d$
- PDE: Determine the region above the $x$-axis for which there is a classical solution.
- Division in differential equations when the dividing function is equal to $0$
Related Questions in REGULARITY-THEORY-OF-PDES
- If $q>p$ then $H^q([0,2\pi])$ is dense in $H^p([0,2\pi])$>
- Motivation to define the boundary value
- 1-D Heat Equation, bounding difference in $\alpha$ given surface temperature
- Implications of weak convergence on the Lebesgue space to Sobolev space
- Harnack type Estimates for a p-Poisson equation with constant source term
- Regularity solution of the Poisson equation with mixed boundary condition
- Intuition for compact embedding of $H^1([0,1])$ in $L^2([0,1])$?
- Young's inequality with duality bracket
- laplace equation $L^p$ estimate
- Interior Gradient Estimate for the p-Elliptic equation
Related Questions in ELLIPTIC-OPERATORS
- If $A$ generates the $C_0$-semigroup $\{T_t;t\ge0\}$, then $Au=f \Rightarrow u=-\int_0^\infty T_t f dt$?
- Definition of constant coefficient elliptic operator
- Why is the index of a harmonic map finite?
- Trilaterating 2D cartesian coordinates, without Z
- Existence and uniqueness of weak solutions to the homogeneous biharmonic equation.
- Counter example to unique solvability of Dirichlet Problem
- Question on why a solution of this PDE is of class $\;C^4\;$
- $\;{u|}_{\partial \Omega} =0\;$ implies $\; \frac{\partial u}{\partial τ}=0\;$
- Definition of a simple characteristic for an elliptic operator
- What does it mean to have a fully nonlinear elliptic PDE?
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?