Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations [PDF]
Revista matemática iberoamericana, 2019 We study various partial data inverse boundary value problems for the semilinear elliptic equation $\Delta u+ a(x,u)=0$ in a domain in $\mathbb R^n$ by using the higher order linearization technique introduced in [LLS 19, FO19].
M. Lassas +3 more
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Infinitely many sign-changing solutions for a semilinear elliptic equation with variable exponent
AIMS Mathematics, 2021 This paper is devoted to study a class of semilinear elliptic equations with variable exponent. By means of perturbation technique, variational methods and a priori estimation, the existence of infinitely many sign-changing solutions to this class of ...
Changmu Chu, Yuxia Xiao , Yanling Xie
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Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities [PDF]
Mathematical Research Letters, 2019 We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain $\Omega\subset \mathbb{R}^n$ which vanish on a closed proper subset of the boundary is dense in $L^1(\Omega)$.
Katya Krupchyk, G. Uhlmann
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010 The basic boundary value problems for semilinear equations of elliptic type with a spectral parameter and discontinuous nonlinearity are considered in a bounded domain with a sufficiently smooth boundary.
Dmitrij К Potapov
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Local minimizers in spaces of symmetric functions and applications [PDF]
, 2014 We study $H^1$ versus $C^1$ local minimizers for functionals defined on spaces of symmetric functions, namely functions that are invariant by the action of some subgroups of $\mathcal{O}(N)$.
Dos Santos +3 more
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Semilinear elliptic equations and supercritical growth
Journal of Differential Equations, 1987 where p p,. The aim of the present paper is to understand, for the case p > pC, the behaviour of solutions to (1 .I ) with large supremum-norm. To this end 0 is restricted to be the unit ball f3c R3, as in this case the behaviour of solutions to (1.1) can be described in some detail.
Budd, C, Norbury, J
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An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds [PDF]
, 2021 Given a conformally transversally anisotropic manifold $(M,g)$, we consider the semilinear elliptic equation $$(-\Delta_{g}+V)u+qu^2=0\quad \text{on $M$}.$$ We show that an a priori unknown smooth function $q$ can be uniquely determined from the knowledge of the Dirichlet-to-Neumann map associated to the semilinear elliptic equation. This extends the
arxiv +1 more source
A new proof of the boundedness results for stable solutions to semilinear elliptic equations [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2019 We consider the class of stable solutions to semilinear equations $-\Delta u=f(u)$ in a bounded smooth domain of $\mathbb{R}^n$. Since 2010 an interior a priori $L^\infty$ bound for stable solutions is known to hold in dimensions $n \leq 4$ for all $C^1$
X. Cabré
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Multiple solutions for a semilinear elliptic equation [PDF]
Transactions of the American Mathematical Society, 1995 Let Ω \Omega be a bounded, smooth domain in R N {\mathbb {R}^N} , N ⩾ 1 N \geqslant 1 . We consider the problem of finding nontrivial solutions to the elliptic boundary value problem \[
Patricio Felmer, Manuel del Pino
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Nonexistence of distributional supersolutions of a semilinear elliptic equation with Hardy potential [PDF]
, 2012 In this paper we study nonexistence of non-negative distributional supersolutions for a class of semilinear elliptic equations involving inverse-square potentials.Comment: Some of the main results are improved.
Fall, Mouhamed Moustapha
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