Geometric intuition for harmonic conjugate functions Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Limit of bounded harmonic functions is harmonicLink between harmonic and holomorphic functions on a non-simply connected domain.harmonic functions on the disk which agree on the real are identical?Given sequence of harmonic functions converges uniformly on compact subsetsCan we deduce maximum modulus theorem for harmonic functions using maximum moduls theorem of complex analysis?Find all harmonic functions of the form $u(x; y) = h(x^2 + y^2).$Complex Analysis - Harmonic function as real part of holomorphic functionharmonic functions, simply connected domains and holomorphyPluriharmonic functions are harmonic on submanifolds?Existence of a Harmonic Conjugate in a Non-Simply Connected Domain
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Geometric intuition for harmonic conjugate functions
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Limit of bounded harmonic functions is harmonicLink between harmonic and holomorphic functions on a non-simply connected domain.harmonic functions on the disk which agree on the real are identical?Given sequence of harmonic functions converges uniformly on compact subsetsCan we deduce maximum modulus theorem for harmonic functions using maximum moduls theorem of complex analysis?Find all harmonic functions of the form $u(x; y) = h(x^2 + y^2).$Complex Analysis - Harmonic function as real part of holomorphic functionharmonic functions, simply connected domains and holomorphyPluriharmonic functions are harmonic on submanifolds?Existence of a Harmonic Conjugate in a Non-Simply Connected Domain
$begingroup$
It is known that given a harmonic function $u$ of class $C ^ 2$ defined in a simply connected subset of $mathbbC$ , we can find a function $v$ also harmonic, such that $f = u + iv$, is a holomorphic function.
What does this definition mean geometrically?
Would there be applications of this in physics?
Comments or references, are very welcome!!
complex-analysis pde harmonic-functions
edited Apr 2 at 0:54
MarianD
2,2761619
asked Apr 2 at 0:36
C. JuniorC. Junior
685412
$endgroup$
add a comment |
$begingroup$
It is known that given a harmonic function $u$ of class $C ^ 2$ defined in a simply connected subset of $mathbbC$ , we can find a function $v$ also harmonic, such that $f = u + iv$, is a holomorphic function.
What does this definition mean geometrically?
Would there be applications of this in physics?
Comments or references, are very welcome!!
complex-analysis pde harmonic-functions
edited Apr 2 at 0:54
MarianD
2,2761619
asked Apr 2 at 0:36
C. JuniorC. Junior
685412
$endgroup$
add a comment |
$begingroup$
It is known that given a harmonic function $u$ of class $C ^ 2$ defined in a simply connected subset of $mathbbC$ , we can find a function $v$ also harmonic, such that $f = u + iv$, is a holomorphic function.
What does this definition mean geometrically?
Would there be applications of this in physics?
Comments or references, are very welcome!!
complex-analysis pde harmonic-functions
edited Apr 2 at 0:54
MarianD
2,2761619
asked Apr 2 at 0:36
C. JuniorC. Junior
685412
$endgroup$
It is known that given a harmonic function $u$ of class $C ^ 2$ defined in a simply connected subset of $mathbbC$ , we can find a function $v$ also harmonic, such that $f = u + iv$, is a holomorphic function.
What does this definition mean geometrically?
Would there be applications of this in physics?
Comments or references, are very welcome!!
complex-analysis pde harmonic-functions
complex-analysis pde harmonic-functions
edited Apr 2 at 0:54
MarianD
2,2761619
asked Apr 2 at 0:36
C. JuniorC. Junior
685412
edited Apr 2 at 0:54
MarianD
2,2761619
asked Apr 2 at 0:36
C. JuniorC. Junior
685412
edited Apr 2 at 0:54
MarianD
2,2761619
edited Apr 2 at 0:54
MarianD
2,2761619
edited Apr 2 at 0:54
MarianD
2,2761619
2,2761619
asked Apr 2 at 0:36
C. JuniorC. Junior
685412
asked Apr 2 at 0:36
C. JuniorC. Junior
685412
asked Apr 2 at 0:36
C. JuniorC. Junior
685412
685412
add a comment |
add a comment |
1 Answer
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Contours of constant $u(x,y)$ and $v(x,y)$ will be crossing orthogonally. For example, the harmonic conjugate of $x$ is $y$.
answered Apr 6 at 13:32
rychrych
2,5561718
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$begingroup$
Contours of constant $u(x,y)$ and $v(x,y)$ will be crossing orthogonally. For example, the harmonic conjugate of $x$ is $y$.
answered Apr 6 at 13:32
rychrych
2,5561718
$endgroup$
add a comment |
$begingroup$
Contours of constant $u(x,y)$ and $v(x,y)$ will be crossing orthogonally. For example, the harmonic conjugate of $x$ is $y$.
answered Apr 6 at 13:32
rychrych
2,5561718
$endgroup$
add a comment |
$begingroup$
Contours of constant $u(x,y)$ and $v(x,y)$ will be crossing orthogonally. For example, the harmonic conjugate of $x$ is $y$.
answered Apr 6 at 13:32
rychrych
2,5561718
$endgroup$
Contours of constant $u(x,y)$ and $v(x,y)$ will be crossing orthogonally. For example, the harmonic conjugate of $x$ is $y$.
answered Apr 6 at 13:32
rychrych
2,5561718
answered Apr 6 at 13:32
rychrych
2,5561718
answered Apr 6 at 13:32
rychrych
2,5561718
answered Apr 6 at 13:32
rychrych
2,5561718
2,5561718
add a comment |
add a comment |
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