Results 11 to 20 of about 343 (50)
Monotonicity of solutions for fractional p-equations with a gradient term
Open Mathematics, 2022 In this paper, we consider the following fractional pp-equation with a gradient term: (−Δ)psu(x)=f(x,u(x),∇u(x)).{\left(-\Delta )}_{p}^{s}u\left(x)=f\left(x,u\left(x),\nabla u\left(x)). We first prove the uniqueness and monotonicity of positive solutions
Wang Pengyan
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A note on an overdetermined problem for the capacitary potential [PDF]
, 2016 We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.Comment: 7 pages. This paper has been written for possible publication in a special volume dedicated to the conference "
Bianchini, Chiara, Ciraolo, Giulio
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Symmetry of solutions to singular fractional elliptic equations and applications
, 2020 In this article, we study the symmetry of positive solutions to a class of singular semilinear elliptic equations whose prototype is (P ) { (−∆)s u = 1 uδ + f (u), u > 0 inΩ; u = 0 in Rn \Ω, where 0 < s < 1, n ≥ 2s, Ω = Br (0) ⊂ Rn , δ > 0, f (u) is a ...
R. Arora +3 more
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A note on Serrin's overdetermined problem [PDF]
, 2014 We consider the solution of the torsion problem $-\Delta u=1$ in $\Omega$ and $u=0$ on $\partial \Omega$. Serrin's celebrated symmetry theorem states that, if the normal derivative $u_\nu$ is constant on $\partial \Omega$, then $\Omega$ must be a ball ...
Ciraolo, Giulio, Magnanini, Rolando
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Old Symmetry Problem Revisited
Open Journal of Mathematical Analysis, 2018 It is proved that if the problem ∇2u = 1 in D, u|S = 0, uN = m := |D|/|S| then D is a ball. There were at least two different proofs published of this result. The proof given in this paper is novel and short.
A. Ramm
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Two optimization problems in thermal insulation [PDF]
, 2017 We consider two optimization problems in thermal insulation: in both cases the goal is to find a thin layer around the boundary of the thermal body which gives the best insulation. The total mass of the insulating material is prescribed..
Bucur, Dorin +2 more
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Global existence and nonexistence of solutions for quasilinear parabolic equation
Boundary Value Problems, 2014 This work is concerned with the global existence and nonexistence of solutions for a quasilinear parabolic equation with null Dirichlet boundary condition.
Xianghui Xu, Yong-Hoon Lee, Z. Fang
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Existence of Ground States of Fractional Schrödinger Equations
Advanced Nonlinear Studies, 2021 We consider ground states of the nonlinear fractional Schrödinger equation with ...
Ma Li, Li Zhenxiong
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The Moving Plane Method for Doubly Singular Elliptic Equations Involving a First-Order Term
Advanced Nonlinear Studies, 2021 In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice ...
Esposito Francesco, Sciunzi Berardino
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A note on the complete rotational invariance of biradial solutions to semilinear elliptic equations [PDF]
, 2010 We investigate symmetry properties of solutions to equations of the form $$ -\Delta u = \frac{a}{|x|^2} u + f(|x|, u)$$ in R^N for $N \geq 4$, with at most critical nonlinearities.
Abatangelo, L., Terracini, S.
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