Semilinear equations with exponential nonlinearity and measure data
Daniele Bartolucci, Fabiana Leoni, Luigi Orsina, Augusto C. Ponce (2005)
Annales de l'I.H.P. Analyse non linéaire
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Daniele Bartolucci, Fabiana Leoni, Luigi Orsina, Augusto C. Ponce (2005)
Annales de l'I.H.P. Analyse non linéaire
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Jarmila Ranošová (1997)
Commentationes Mathematicae Universitatis Carolinae
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Let , , be the -dimensional unit sphere, be the surface measure on and . We characterize all subsets of such that for every positive solution of the Helmholtz equation on . A closely related problem of representing functions of as sums of blocks of the form corresponding to points of is also considered. The results provide a counterpart to results for classical harmonic functions in a ball, and for parabolic functions on a slab, see References.
Stefan Krömer (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We derive sharp necessary conditions for weak sequential lower semicontinuity of integral functionals on Sobolev spaces, with an integrand which only depends on the gradient of a scalar field over a domain in . An emphasis is put on domains with infinite measure, and the integrand is allowed to assume the value .
Farag, Hany M. (2000)
Annales Academiae Scientiarum Fennicae. Mathematica
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Saksman, Eero (1999)
Annales Academiae Scientiarum Fennicae. Mathematica
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Lewis, John L., Vogel, Andrew L. (2007)
Boundary Value Problems [electronic only]
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Ebenfelt, P., Khavinson, D., Shapiro, H. S. (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Miloš Arsenović, Romi F. Shamoyan (2013)
Kragujevac Journal of Mathematics
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