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If $A$ generates the $C_0$-semigroup $\{T_t;t\ge0\}$, then $Au=f \Rightarrow u=-\int_0^\infty T_t f dt$?

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#functional-analysis #partial-differential-equations #elliptic-equations #semigroup-of-operators #elliptic-operators
200
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Definition of constant coefficient elliptic operator

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#partial-differential-equations #elliptic-equations #elliptic-operators
2.6k
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Weak formulation of Robin boundary condition problem

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#functional-analysis #partial-differential-equations #sobolev-spaces #calculus-of-variations #elliptic-equations
150
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Harmonic functions satisfying given inequality

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#functional-analysis #partial-differential-equations #harmonic-functions #elliptic-equations
244
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How to get the equation of an ellipse given the center, directrix and length of latus rectum?

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#elliptic-equations
136
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Regularity of the Divergence of Weak Solutions to Elliptic PDEs

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#integration #sobolev-spaces #weak-derivatives #elliptic-equations
242
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Showing that a function is harmonic

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#complex-analysis #harmonic-functions #conformal-geometry #elliptic-equations #potential-theory
522
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Define a "Neumann" trace of a harmonic function on bounded domain

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#partial-differential-equations #elliptic-equations #trace-map
149
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How to determine if elliptic equation comes from variational problem?

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#partial-differential-equations #calculus-of-variations #elliptic-equations
39.9k
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What is the parametric equation of a rotated Ellipse (given the angle of rotation)

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#rotations #parametric #elliptic-equations
59
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how to solve a linear pde of changing evolution equation?

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#partial-differential-equations #elliptic-equations #linear-pde
376
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Is it possible to explicitly solve the inhomogeneous Helmholtz equation in a rectangle?

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#partial-differential-equations #eigenfunctions #elliptic-equations
158
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Counter example to unique solvability of Dirichlet Problem

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#partial-differential-equations #elliptic-equations #elliptic-operators
78
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Young's inequality with duality bracket

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#real-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #elliptic-equations
66
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Question on why a solution of this PDE is of class $\;C^4\;$

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#functional-analysis #partial-differential-equations #estimation #elliptic-equations #elliptic-operators

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