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A chain rule in L1 (div;Q) and its applications to lower - download pdf or read online

By De Cicco V., De Leoni G.

A series rule within the area L1 (div;Ω) is received lower than vulnerable regularity conditions.This chain rule has vital purposes within the examine of decrease semicontinuityproblems for basic functionals of the shape ☺Ω f(x, u,∇u) dx with admire to powerful convergence in L1 (Ω) . Classical result of Serrin and of De Giorgi, Buttazzo and Dal Maso are prolonged and generalized.

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Planet called Gliese 581d A is the closest they ’ve found yet. Astronomers first discovered planets around the star Gliese 581 (lower right) in 2007. 41 Scientists are pretty sure they know how our solar system formed. 6 billion years ago, the Sun was surrounded by a disk of dust and gas left over from its formation. As the disk rotated, it got flatter and thinner, just as pizza dough gets flatter and thinner as a pizza maker spins it around. Particles of dust in the spinning disk stuck together and formed clumps.

The planet is seven Seven Wonders beyond the Solar System This illustration shows the planet orbiting 51 Pegasi. The planet is probably a hot ball of molten rock. 44 In this illustration, the large object at right is the planet orbiting 70 Virginis. 70 Virginis itself is the bright star at left. It shines from behind one of the planet’s moons. The Most Earthlike Extrasolar Planet times wider than Earth, but it is far too small to be a brown dwarf. It orbits very close to 51 Pegasi. 3 million miles (7 million km) away.

As a red giant enters the final stages of its life, its thin, red-glowing atmosphere begins to drift off into space. The inner core, which still contains most of the mass of the original star, slowly shrinks. As it does, it gets hotter. Eventually, most of the elements in the star turn into iron. The star can go no further than this. Fusion stops. The star is like a chunk of coal that has burned into a cinder. The star has no source of energy left to counterbalance the force of gravity. The star begins to contract rapidly.

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A chain rule in L1 (div;Q) and its applications to lower semicontinuity by De Cicco V., De Leoni G.


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