Results 1  10
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54
Local pointwise estimates for solutions of the σ2 curvature equation on 4 manifolds
, 2004
"... ..."
The AllegrettoPiepenbrink Theorem for Strongly Local Dirichlet Forms
 DOCUMENTA MATH.
, 2009
"... The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator. ..."
Abstract

Cited by 7 (4 self)
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The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator.
Ground state alternative for pLaplacian with potential term, http://arxiv.org/PS cache/math/pdf/0511/0511039.pdf
"... term ..."
On the location of concentration points for singularly perturbed elliptic equations, preprint
"... Abstract. By exploiting a variational identity of PohoˇzaevPucciSerrin type for solutions of class C 1, we get some necessary conditions for locating the peakpoints of a class of singularly perturbed quasilinear elliptic problems in divergence form. More precisely, we show that the points where ..."
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Cited by 5 (4 self)
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Abstract. By exploiting a variational identity of PohoˇzaevPucciSerrin type for solutions of class C 1, we get some necessary conditions for locating the peakpoints of a class of singularly perturbed quasilinear elliptic problems in divergence form. More precisely, we show that the points where the concentration occurs, in general, must belong to what we call the set of weakconcentration points. Finally, in the semilinear case, we provide a new necessary condition which involves the Clarke subdifferential of the groundstate function. 1.
Nonlinear Hodge maps
 J. Math. Phys
, 2000
"... We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under w ..."
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Cited by 5 (5 self)
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We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Continuity results are given for the transonic limit, highdimensional flow, and flow having positive vorticity. The gradient flow of solutions is estimated. Implications for other quasilinear field theories are suggested. 1 Introduction: nonlinear Hodge
SPIKE SOLUTIONS FOR A CLASS OF SINGULARLY PERTURBED QUASILINEAR ELLIPTIC EQUATIONS
, 2003
"... Abstract. By means of a penalization scheme due to del Pino and Felmer, we prove the existence of single–peaked solutions for a class of singularly perturbed quasilinear elliptic equations associated with functionals which lack of smoothness. We don’t require neither uniqueness assumptions on the li ..."
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Cited by 4 (1 self)
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Abstract. By means of a penalization scheme due to del Pino and Felmer, we prove the existence of single–peaked solutions for a class of singularly perturbed quasilinear elliptic equations associated with functionals which lack of smoothness. We don’t require neither uniqueness assumptions on the limiting autonomous equation nor monotonicity conditions on the nonlinearity. Compared with the semilinear case some difficulties arise and the study of concentration of the solutions needs a somewhat involved analysis in which the Pucci–Serrin variational identity plays an important role.
SEMISTABLE AND EXTREMAL SOLUTIONS OF REACTION EQUATIONS INVOLVING THE pLAPLACIAN
"... We consider nonnegative solutions of −∆pu = f(x, u), where p> 1 and ∆p is the pLaplace operator, in a smooth bounded domain of RN with zero Dirichlet boundary conditions. We introduce the notion of semistability for a solution (perhaps unbounded). We prove that certain minimizers, or onesided mini ..."
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Cited by 4 (0 self)
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We consider nonnegative solutions of −∆pu = f(x, u), where p> 1 and ∆p is the pLaplace operator, in a smooth bounded domain of RN with zero Dirichlet boundary conditions. We introduce the notion of semistability for a solution (perhaps unbounded). We prove that certain minimizers, or onesided minimizers, of the energy are semistable, and study the properties of this class of solutions. Under some assumptions on f that make its growth comparable to um, we prove that every semistable solution is bounded if m < mcs. Here, mcs = mcs(N, p) is an explicit exponent which is optimal for the boundedness of semistable solutions. In particular, it is bigger than the critical Sobolev exponent p ∗ − 1. We also study a type of semistable solutions called extremal solutions, for which we establish optimal L ∞ estimates. Moreover, we characterize singular extremal solutions by their semistability property when the domain is a ball and 1 < p < 2.
I.: Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms
"... Abstract. We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples. ..."
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Cited by 4 (3 self)
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Abstract. We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples.
P.: SobolevPoincar'e inequalities for p ! 1
 Ind. Univ. Math. J
, 1994
"... Abstract. If Ω is a John domain (or certain more general domains), and ∇u  satisfies a certain mild condition, we show that u ∈ W 1,1 `R loc (Ω) satisfies a SobolevPoincaré inequality Ω u − aq ´ 1/q ..."
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Cited by 3 (2 self)
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Abstract. If Ω is a John domain (or certain more general domains), and ∇u  satisfies a certain mild condition, we show that u ∈ W 1,1 `R loc (Ω) satisfies a SobolevPoincaré inequality Ω u − aq ´ 1/q
Multipeak solutions for a class of degenerate elliptic problems, Asymptotic Anal
"... Abstract. By means of a penalization argument due to del Pino and Felmer, we prove the existence of multi–spike solutions for a class of quasilinear elliptic equations under natural growth conditions. Compared with the semilinear case some difficulties arise, mainly concerning the properties of the ..."
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Cited by 3 (3 self)
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Abstract. By means of a penalization argument due to del Pino and Felmer, we prove the existence of multi–spike solutions for a class of quasilinear elliptic equations under natural growth conditions. Compared with the semilinear case some difficulties arise, mainly concerning the properties of the limit equation. The study of concentration of the solutions requires a somewhat involved analysis in which a Pucci–Serrin type identity plays an important role. 1. Introduction and