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Relaxation for Dirichlet Problems Involving a Dirichlet Form
Zeitschrift für Analysis und ihre Anwendungen, 2000For a fixed Dirichlet form, we study the space of positive Borel measures (possibly infinite) which do not charge polar sets. We prove the density in this space of the set of the measures which represent varying, domains. Our method is constructive. For the Laplace operator, the proof was based on a pavage of the space.
BIROLI, MARCO, TCHOU N.
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A recurrence for Dirichlet problems
Computing, 1982The formal integration of the differential eq. to an integral equation allows the iterative construction of a class of “basic” functions which, characterized by the kernel, are suitable for developing the solution to the boundary value problem.
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Superlinear Dirichlet problems
Nonlinear Analysis: Theory, Methods & Applications, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2001
In its simplest form the Dirichlet problem may be stated as follows: for a given function \( f \in C\left( {{\partial ^\infty }\Omega } \right)\), determine, if possible, a function h ∈ H(Ω) such that h(x) → f(y) as x → y for each \( y \in {\partial ^\infty }\Omega \).
David H. Armitage, Stephen J. Gardiner
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In its simplest form the Dirichlet problem may be stated as follows: for a given function \( f \in C\left( {{\partial ^\infty }\Omega } \right)\), determine, if possible, a function h ∈ H(Ω) such that h(x) → f(y) as x → y for each \( y \in {\partial ^\infty }\Omega \).
David H. Armitage, Stephen J. Gardiner
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2014
The natural Dirichlet problem in C n is not the classical one for solutions of the Laplace equation but rather for solutions of the Monge–Ampere equation. We present the solution of this Dirichlet problem in a ball.
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The natural Dirichlet problem in C n is not the classical one for solutions of the Laplace equation but rather for solutions of the Monge–Ampere equation. We present the solution of this Dirichlet problem in a ball.
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Theoretical and Mathematical Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2009
In this chapter, approximation of solutions of Laplace’s equation requires the study of sequences of harmonic functions, making use of the integral representations and averaging properties of harmonic functions. The latter property is used to incorporate a larger class of functions called superharmonic functions that are used to approximate solutions ...
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In this chapter, approximation of solutions of Laplace’s equation requires the study of sequences of harmonic functions, making use of the integral representations and averaging properties of harmonic functions. The latter property is used to incorporate a larger class of functions called superharmonic functions that are used to approximate solutions ...
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The Dirichlet Problem for a Hyperbolic Equation
American Journal of Mathematics, 1941Es wird das Problem behandelt, ein solches Paar stetiger Funktionen \( f(x), g(y) \), \( (a \leqq x \leqq b, \alpha \leqq y \leqq \beta) \) zu finden, daß \( f(x)+g(y) \) gegebene stetige Werte \( v \) auf dem Rand \( C \) eines gegebenen, im Rechtecke \( a \leqq x \leqq b, \alpha \leqq y \leqq \beta \) enthaltenen konvexen Bereiches \( B \) annimmt ...
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