Two positive solutions for a Dirichlet problem with the (p,q) ‐Laplacian
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DOI: 10.1002/mana.201800330
Abstract: The aim of this paper is to prove the existence of two solutions for a nonlinear elliptic problem involving the (p,q) ‐Laplacian operator. The solutions are obtained by using variational methods and critical points theorems.… read more here.
Keywords: problem laplacian; solutions dirichlet; positive solutions; problem ... See more keywords
Fredholmness of the Dirichlet Problem for 2m$$ 2m $$th‐Order Elliptic Equations in Grand Sobolev Spaces
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DOI: 10.1002/mma.11098
Abstract: In this paper, on a bounded domain with a sufficiently smooth boundary , it is considered a uniformly elliptic equation of th order, the coefficients of which are continuous in the principal part. Grand Lebesgue… read more here.
Keywords: space; dirichlet problem; grand sobolev; order ... See more keywords
The abstract Dirichlet problem for continuous vector-valued functions
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DOI: 10.1007/s00013-016-1015-y
Abstract: Let X be a simplex with the set $${\text {ext}}\, X$$extX of extreme points being Lindelöf. We show that a continuous bounded mapping defined on $${\text {ext}}\, X$$extX with values in a Fréchet space F… read more here.
Keywords: dirichlet problem; continuous vector; vector valued; abstract dirichlet ... See more keywords
Harmonic measure and quantitative connectivity: geometric characterization of the $$L^p$$-solvability of the Dirichlet problem
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DOI: 10.1007/s00222-020-00984-5
Abstract: Let $\Omega\subset\mathbb R^{n+1}$ be an open set with $n$-AD-regular boundary. In this paper we prove that if the harmonic measure for $\Omega$ satisfies the so-called weak-$A_\infty$ condition, then $\Omega$ satisfies a suitable connectivity condition, namely… read more here.
Keywords: dirichlet problem; geometric characterization; connectivity; condition ... See more keywords
Integral Equation Formulation of the Biharmonic Dirichlet Problem
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DOI: 10.1007/s10915-017-0559-8
Abstract: We present a novel integral representation for the biharmonic Dirichlet problem. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman–Lauricella integral representation can be used.… read more here.
Keywords: dirichlet problem; problem; integral representation; biharmonic dirichlet ... See more keywords
Existence of Solution of the Dirichlet Problem for the Heat-Conduction Equation with General Stochastic Measure
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DOI: 10.1007/s10958-019-04351-5
Abstract: We present sufficient conditions for the existence of a weak solution of the Dirichlet problem for the heat-conduction equation with random action described by an integral over the general stochastic measure. read more here.
Keywords: problem heat; dirichlet problem; solution dirichlet; heat conduction ... See more keywords
Uniform approximation by harmonic polynomials for solving the Dirichlet problem of Laplace’s equation on a disk
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DOI: 10.1007/s10986-025-09673-3
Abstract: In this paper, we study the Dirichlet problem for Laplace’s equation in an open disk. The uniqueness of solutions is ensured by the well-known weak maximum principle. We introduce a novel approach to demonstrate the… read more here.
Keywords: laplace equation; problem laplace; disk; harmonic polynomials ... See more keywords
Sobolev–Dirichlet problem for quasilinear elliptic equations in generalized Orlicz–Sobolev spaces
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DOI: 10.1007/s11117-020-00789-z
Abstract: In this paper, we prove existence, uniqueness, and local regularity of the solution to the Sobolev–Dirichlet problem for quasilinear elliptic equations in the generalized Orlicz–Sobolev spaces on domains, not necessarily bounded, of $${\mathbb {R}}^N$$ .… read more here.
Keywords: sobolev dirichlet; dirichlet problem; elliptic equations; problem quasilinear ... See more keywords
Existence and uniqueness results in weighted spaces for Dirichlet problem in unbounded domains
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DOI: 10.1007/s11587-019-00465-9
Abstract: We study the Dirichlet problem for a second order linear elliptic partial differential equation with discontinuous coefficients in unbounded domains. We establish an existence and uniqueness result. read more here.
Keywords: dirichlet problem; unbounded domains; existence uniqueness; uniqueness results ... See more keywords
Dirichlet problem and subclasses of Baire-one functions
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DOI: 10.1007/s11856-018-1707-z
Abstract: Let U be a bounded open subset of ℝd, d ≥ 2 and f ∈ C(∂U). The Dirichlet solution fCU of the Dirichlet problem associated with the Laplace equation with a boundary condition f is… read more here.
Keywords: space; dirichlet; dirichlet problem; one functions ... See more keywords
A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane
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DOI: 10.1016/j.jmaa.2018.04.045
Abstract: Abstract A new proof is given of a simple probabilistic lemma which implies the solution of the Dirichlet problem for simply connected domains in the plane. This proof uses the conformal invariance of planar Brownian… read more here.
Keywords: dirichlet problem; domains plane; solution dirichlet; connected domains ... See more keywords