Geodesic
Reduced Measures Associated with Parabolic Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 10-31.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the existence and the properties of reduced measures for the parabolic equations $\partial_tu-\Delta u+g(u)=0$ in $\Omega\times(0,\infty)$ subject to the conditions (P): $u=0$ on $\partial\Omega\times(0,\infty)$, $u(x,0)=\mu$ and (P$'$): $u=\mu'$ on $\partial\Omega\times(0,\infty)$, $u(x,0)=0$, where $\mu$ and $\mu'$ are positive Radon measures and $g$ is a continuous nondecreasing function. 
@article{TM_2008_260_a1,
     author = {W. Al Sayed and M. Jazar and L. V\'eron},
     title = {Reduced {Measures} {Associated} with {Parabolic} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {10--31},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_260_a1/}
}
TY  - JOUR
AU  - W. Al Sayed
AU  - M. Jazar
AU  - L. Véron
TI  - Reduced Measures Associated with Parabolic Problems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2008
SP  - 10
EP  - 31
VL  - 260
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2008_260_a1/
LA  - en
ID  - TM_2008_260_a1
ER  - 
%0 Journal Article
%A W. Al Sayed
%A M. Jazar
%A L. Véron
%T Reduced Measures Associated with Parabolic Problems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2008
%P 10-31
%V 260
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2008_260_a1/
%G en
%F TM_2008_260_a1
W. Al Sayed; M. Jazar; L. Véron. Reduced Measures Associated with Parabolic Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 10-31. http://geodesic.mathdoc.fr/item/TM_2008_260_a1/

[1] Baras P., Pierre M., “Problèmes paraboliques semi-linéaires avec données mesures”, Appl. Anal., 18 (1984), 111–149 | DOI | MR | Zbl

[2] Brézis H., Friedman A., “Nonlinear parabolic equations involving measures as initial conditions”, J. Math. Pures et Appl., 62 (1983), 73–97 | MR | Zbl

[3] Brézis H., Marcus M., Ponce A. C., “Nonlinear elliptic equations with measures revisited”, Mathematical aspects of nonlinear dispersive equations, Ann. Math. Stud., 163, Princeton Univ. Press, Princeton, 2007, 55–109 | MR | Zbl

[4] Brézis H., Ponce A. C., “Reduced measures on the boundary”, J. Funct. Anal., 229:1 (2005), 95–120 | DOI | MR | Zbl

[5] de la Vallée Poussin C., “Sur l'intégrale de Lebesgue”, Trans. Amer. Math. Soc., 16 (1915), 435–501 | DOI | MR | Zbl

[6] Dávila J., Ponce A. C., “Variants of Kato's inequality and removable singularities”, J. Anal. Math., 91 (2003), 143–178 | DOI | MR | Zbl

[7] Marcus M., Véron L., “Initial trace of positive solutions of some nonlinear parabolic equations”, Commun. Part. Diff. Equat., 24 (1999), 1445–1499 | DOI | MR | Zbl

[8] Marcus M., Véron L., “Semilinear parabolic equations with measure boundary data and isolated singularities”, J. Anal. Math., 85 (2001), 245–290 | DOI | MR | Zbl

[9] Marcus M., Véron L., “Trace au bord latéral des solutions positives d'équations paraboliques non linéaires”, C. r. Acad. sci. Paris. Sér. 1, 324:7 (1997), 783–788 | MR | Zbl

[10] Marcus M., Véron L., “Initial trace of positive solutions to semilinear parabolic inequalities”, Adv. Nonlin. Stud., 2:4 (2002), 395–436 | MR | Zbl

[11] Vazquez J. L., “On a semilinear equation in $\mathbb R^2$ involving bounded measures”, Proc. Roy. Soc. Edinburgh A, 95 (1983), 181–202 | MR | Zbl