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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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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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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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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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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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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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1991
This chapter is devoted to studying boundary value problems for second-order elliptic equations. The variational (also known as Hilbert space) approach to the Dirichlet problem is emphasized. Maximum principles are discussed in §5.10 and §5.11, which are independent of the preceding sections and are essential reading along with §5.1, §5.2, and §5.3 ...
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This chapter is devoted to studying boundary value problems for second-order elliptic equations. The variational (also known as Hilbert space) approach to the Dirichlet problem is emphasized. Maximum principles are discussed in §5.10 and §5.11, which are independent of the preceding sections and are essential reading along with §5.1, §5.2, and §5.3 ...
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