Radially increasing minimizing surfaces or deformations under pointwise constraints on positions and gradients |
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Authors: | Luís Balsa Bicho António Ornelas |
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Institution: | aCima-ue, Rua Romão Ramalho 59, Évora, Portugal |
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Abstract: | In this paper, we prove existence of radially symmetric minimizersuA(x)=UA(|x|), having UA(⋅)AC monotone and increasing, for the convex scalar multiple integral(∗ ) among those u(⋅) in the Sobolev space. Here, |∇u(x)| is the Euclidean norm of the gradient vector and BR is the ball ; while A is the boundary data.Besides being e.g. superlinear (but no growth needed if (∗) is known to have minimum), our Lagrangian?∗∗:R×R→0,∞] is just convex lsc and and ?∗∗(s,⋅) is even; while ρ1(⋅) and ρ2(⋅) are Borel bounded away from .Remarkably, (∗) may also be seen as the calculus of variations reformulation of a distributed-parameter scalar optimal control problem. Indeed, state and gradient pointwise constraints are, in a sense, built-in, since ?∗∗(s,v)=∞ is freely allowed. |
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Keywords: | MSC: 49J10 49N60 |
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